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(CBS) Getting a peace deal in the Middle East is such a priority to President Obama that his first foreign calls on his first day in office were to Arab and Israeli leaders. And on day two, the president made former Senator George Mitchell his special envoy for Middle East peace. Mr. Obama wants to shore up the ceasefire in Gaza, but a lasting peace really depends on the West Bank where Palestinians had hoped to create their state. The problem is, even before Israel invaded Gaza, a growing number of Israelis and Palestinians had concluded that peace between them was no longer possible, that history had passed it by. For peace to have a chance, Israel would have to withdraw from the West Bank, which would then become the Palestinian state.

It’s known as the "two-state" solution. But, while negotiations have been going on for 15 years, hundreds of thousands of Jewish settlers have moved in to occupy the West Bank. Palestinians say they can't have a state with Israeli settlers all over it, which the settlers say is precisely the idea.

Daniella Weiss moved from Israel to the West Bank 33 years ago. She has been the mayor of a large settlement.

"I think that settlements prevent the establishment of a Palestinian state in the land of Israel. This is the goal. And this is the reality," Weiss told 60 Minutes correspondent Bob Simon.

Though settlers and Palestinians don't agree on anything, most do agree now that a peace deal has been overtaken by events.

"While my heart still wants to believe that the two-state solution is possible, my brain keeps telling me the opposite because of what I see in terms of the building of settlements. So, these settlers are destroying the potential peace for both people that would have been created if we had a two-state solution," Dr. Mustafa Barghouti, once a former candidate for Palestinian president, told Simon.

And he told 60 Minutes Israel's invasion of Gaza - all the death and destruction in response to rockets from Hamas - convinces him that Israel does not want a two-state solution. "My heart is deeply broken, and I am very worried that what Israel has done has furthered us much further from the possibility of [a] two-state solution."

Palestinians had hoped to establish their state on the West Bank, an area the size of Delaware. But Israelis have split it up with scores of settlements, and hundreds of miles of new highways that only settlers can use. Palestinians have to drive - or ride - on the older roads.

When they want to travel from one town to another, they have to submit to humiliating delays at checkpoints and roadblocks. There are more than 600 of them on the West Bank.

Asked why there are so many checkpoints, Dr. Barghouti said, "I think the main goal is to fragment the West Bank. Maybe a little bit of them can be justified because they say it's for security. But I think the vast majority of them are basically to block the movement of people from one place to another."

Here's how they block Barghouti: he was born in Jerusalem, grew up in Jerusalem and worked in a hospital there for 14 years. Four years ago he moved to a town just 10 miles away, but now, because he no longer lives in Jerusalem, he can't get back in - ever.

He says he can't get a permit to go. "I asked for a permit to go to Jerusalem during the last year, the last years about 16 times. And 16 times they were rejected. Like most Palestinians, I don't have a permit to go to the city I was born in, to the city I used to work in, to the city where my sister lives."

What he's up against are scores of Israeli settlements dominating the lowlands like crusader fortresses. Many are little cities, and none of them existed 40 years ago. The Israelis always take the high ground, sometimes the hills, and sometimes the homes. And sometimes Arabs are occupied inside their own homes.

One house for example is the highest house on the highest hill overlooking the town of Nablus. 60 Minutes learned that Israeli soldiers often corral the four families who live there and take over the house to monitor movement down below.

Simon and the 60 Minutes team went to an apartment owned by a Mr. Nassif. That morning, Israeli soldiers had apparently entered the apartment, without notice, and remained there when Simon knocked on the door.

"We cannot speak with you, there are soldiers," Nassif told Simon. "We are in prison here."

Asked what was happening, Nassif says, "They are keeping us here and the soldiers are upstairs, we cannot move. We cannot speak with you."

Nassif said he couldn't leave the house and didn't know how long he'd have to stay in place. Asked if they were paying him any money, he told Simon, "You are kidding?"

Abdul Nassif, a bank manager said he had to get to his bank to open the safe, but one of the soldiers wouldn't let him go. He told 60 Minutes whenever the soldiers come they wake everybody up, and herd them into a kitchen for hours while soldiers sleep in their beds. They can't leave or use the phone, or let 60 Minutes in.

(CBS) He sent 60 Minutes downstairs to see if his brother would open the door so we could ask the soldiers why they keep taking over this house. But the brother told Simon, "The soldiers close the door from the key. They take the key."

So Simon and the crew left, and that night, so did the soldiers. But when 60 Minutes returned two days later, the soldiers were back for more surveillance. This time they kept the women under house arrest, but let the men go to work and the children go to school. When the children returned, we caught a glimpse of two armed soldiers at the top of the stairs.

Then more children came home, but the soldiers wouldn't open the door again.

A commander told Simon that he and the crew would have to go back behind a wall in order for the children to be let in.

The commander declined to talk to 60 Minutes. "But we are talking to you now," Simon pointed out, standing outside. "Why don't you tell us what you are doing here? Have you lost your voice? Well they've closed the door now, they've closed the window so I guess if the children are going to get home now we have to leave, so that is what we will do."

An army spokesperson told us the army uses the Nassifs' house for important surveillance operations. The Nassifs told 60 Minutes that soldiers usually stay for a day or two, always coming and going in the middle of the night. When they do go, the Nassifs never know when they will be occupied again. It could be tomorrow, next week, or next month. The only certainty, they say, is that the soldiers will be back.

Another crippling reality on the West Bank is high unemployment, now about 20 percent. So some Palestinians can only find jobs building Israeli settlements. They're so ashamed to work on the construction sites that they asked 60 Minutes not to show their faces.

The settlers now number 280,000, and as they keep moving in, their population keeps growing about five percent every year. But the 2.5 million Arabs have their strategy too: they're growing bigger families.

Demographers predict that within ten years Arabs will outnumber Jews in Israel, the West Bank and Gaza. Without a separate Palestinian state the Israelis would have three options, none of them good. They could try ethnic cleansing, drive the Palestinians out of the West Bank, or they could give the Palestinians the vote. That would be the democratic option but it would mean the end of the Jewish state. Or they could try apartheid - have the minority Israelis rule the majority Palestinians, but apartheid regimes don't have a very long life.

"Unfortunately, and I have to say to you that apartheid is already in place," Dr. Barghouti argued.

(CBS) Apartheid? Israel is building what it calls a security wall between the West Bank and Israel to stop suicide bombers. The Palestinians are furious because it appropriates eight percent of the West Bank. Not only that. It weaves its way through Palestinian farms, separating farmers from their land. They have to wait at gates for soldiers to let them in. Settlers get a lot more water than Palestinians, which is why settlements are green and Arab areas are not.

Moderate Israelis who deplore the occupation used to believe passionately in a two-state solution. That is no longer the case.

Meron Benvenisti used to be deputy mayor of Jerusalem. He told Simon the prospects of the two-state solution becoming a reality are "nil."

"The geopolitical condition that’s been created in '67 is irreversible. Cannot be changed. You cannot unscramble that egg," he explained.

Asked if this means the settlers have won, Benvenisti told Simon, "Yes."

"And the settlers will remain forever and ever?" Simon asked.

"I don't know forever and ever, but they will remain and will flourish," Benvenisti said.

"The settlers, the attitude that I present here, this is the heart. This is the pulse. This is the past, present, and future of the Jewish state," Daniella Weiss told Simon.

She says the she and the settlers are immovable. "We will stay here forever."

But one very important Israeli says she intends to move them out. She's Foreign Minister Tzipi Livni, a candidate to become prime minister in elections next month. She's also Israel’s chief negotiator with the Palestinians, and she told 60 Minutes peace is unthinkable with the settlers where they are.

"Can you really imagine evacuating the tens of thousands of settlers who say they will not leave?" Simon asked.

"It's not going to be easy. But this is the only solution," she replied.

"But you know that there are settlers who say, 'We will fight. We will not leave. We will fight,'" Simon asked.

"So this is the responsibility of the government and police to stop them. As simple as that. Israel is a state of law and order," Livni said.

(CBS) It's also a state of law and disorder. When the army evicted just nine families from a West Bank settlement called Amona three years ago, it was chaos. It was the first time since the creation of the state that Jews were in pitched battles against Jews. To Israelis of all stripes, it was not a pretty picture. And it made the government loath to try again.

Officials fear that more battles to empty settlements could rip Israel apart. They're afraid that religious officers in the army - and there are an increasing number of them - would disobey any order to evict settlers.

The army is evicting Arabs from their homes in East Jerusalem, which Palestinians hoped to make their capital. Outraged, Arabs tried to save their homes, but the Israelis have the guns. Israel demolished more than 100 Arab homes in the past year, ruling they had been illegally built. Arabs say this is just another tactic to drive them out. But officials say they also knock down unauthorized Jewish buildings on the West Bank. They're put up by youngsters, the next generation’s campaign to populate the land.

Daniella Weiss told 60 Minutes they will not be stopped.

Despite the army tearing down a structure, the settlers began rebuilding it on the same day. "We will have the upper hand," Weiss vowed.

"But the army will tear it down again," Simon pointed out.

"And we will rebuild it," Weiss said. "The experience shows that the world belongs to those who are stubborn, and we are very stubborn."

Stubborn, she says, because they were ordered to populate this land by no less an authority than God. "This is the mission of our generation and I want to emphasis the most important point is to this," Weiss said, picking up some soil, "to hold strong to the soil of the Holy Land."