At the eastern tip of the Israeli settlement of Ariel, cranes and earth-movers are at work on the college campus, which stretches across a hill overlooking the villages and valleys of the West Bank. Eleven miles from the internationally recognised Green Line separating Israel from the Palestinian Territories, construction is under way of buildings to accommodate a projected growth from 13,000 to 20,000 students over the next 10 years.

In September, the college passed a significant milestone when the Israeli cabinet voted to upgrade the college to a university as a matter of "national importance". Backing the move, prime minister Binyamin Netanyahu told the cabinet that Ariel was "an inseparable part of Israel" and would remain so in the future.

The decision, concerning a settlement which is illegal under international law and whose future is a key determinant of a viable Palestinian state and the peaceful resolution of a decades-old conflict, was not universally acclaimed. Urging Israel to reconsider, British foreign secretary William Hague said it would "deepen the presence of the settlements in the Palestinian territories and will create another obstacle to peace".

Deeper inside the West Bank, a few miles east of Ariel, construction workers are also busy. Earlier this year, Israel approved plans for 600 homes in the settlement of Shiloh and its outpost, Shvut Rachel. "This community has doubled in size in 20 years, and there is no question that there will be further growth. The demand for homes is much greater than supply," said Shiloh's former mayor, David Rubin.

Further south, Israel a year ago announced plans for a settlement across the Green Line close to Jerusalem. The 2,600 homes of Givat Hamatos, plus expansion of neighbouring Gilo and Har Homa, will increase the separation of Palestinian areas of the city from the West Bank, reducing the likelihood of East Jerusalem becoming the capital of a future Palestinian state.

These three places illustrate a pattern of settlement growth that mocks Barack Obama's demand, issued early in his presidency, that Israel should halt expansion as an impediment to peace.

Entrenchment of "facts on the ground" has led a growing number of people, on both sides of the conflict, to declare that creating a Palestinian state alongside an Israeli state to resolve the conflict is now impossible. The "two-state solution", they say, is dead.

In June 2009, less than six months into his presidency, Obama addressed the Israeli-Palestinian conflict in his keynote speech on the Middle East in Cairo. Restating US commitment to a two-state model, he said the Palestinians must abandon violence, and develop their capacity to govern. By most reckoning, the Ramallah leadership has ticked both boxes.

On the Israeli side, Obama said the US did not accept the legitimacy of Jewish settlements. "It is time for these settlements to stop," he said bluntly.

There followed protracted negotiations between the US and Israeli governments which resulted, in November 2009, in Netanyahu reluctantly acceding to a temporary construction freeze in West Bank settlements. East Jerusalem was exempt, with the completion of any buildings whose foundations were already laid. In anticipation of the moratorium, the number of construction starts rose significantly in the run-up to November.

Critics denounced the freeze as a farce, but the settlers were incensed and relations between Netanyahu and Obama nosedived. Relations between the two allies were "in the state of a tectonic rift in which continents are drifting apart," Michael Oren, Israel's ambassador to the US, memorably said in mid-2010. The freeze ended in September 2010, despite US efforts to secure an extension. Direct talks between Israel and the Palestinians swiftly broke down as settlement construction resumed, since when the "peace process" has been in a catatonic state.

Obama was heavily criticised for his early focus on settlements. But, according to one observer, "the problem was not Obama's identification of the settlement issue as a critical obstacle to the resumption of talks and, beyond that, to the two-state model itself – it was his failure to stick with it in the face of Netanyahu's intransigence".

In the past two years, US officials have issued routine condemnation of settlement expansion plans but real pressure from Washington has eased. In June, Israel's Central Bureau of Statistics reported that the number of Jewish settlers in the West Bank had risen by 15,000 over the previous 12 months, to a record 350,000. Most of the growth was in small hardline settlements deep inside the West Bank. An additional 200,000 Jews live in settlements in East Jerusalem. In the New York Times, s ettlers' leader Dani Dayon pronounced the Jewish presence across the Green Line "an irreversible fact". Predicting the numbers in Jewish colonies in the West Bank would top 400,000 by 2014, he wrote: "Trying to stop settlement expansion is futile." The international community should relinquish its "vain attempts to attain the unattainable two-state solution".

He said: "Our presence here has now passed a point of non-return. It's irrevocable, a fait accompli." The status quo, while not ideal, was "immeasurably better than any feasible alternative".

In the face of the "facts on the ground", others are proposing alternative courses of action. Some on the Israeli right have called for annexation of the West Bank. The Palestinian population can either accept living under Israeli rule with limited rights or leave, they say. Critics say this would be akin to apartheid and make Israel a pariah state.

Others have called for a more modest, but unilateral, annexation of the 9.4% of the West Bank which will lie between the Green Line and Israel's separation barrier when it is complete. Defence minister Ehud Barak recently proposed that settlers outside the three main blocs – Ma'ale Adumim, Gush Etzion and Ariel – should be evacuated or choose to live under Palestinian rule. The barrier would become what its critics have always charged – Israel's new border. "It would be best to reach agreement with the Palestinians but, barring that, practical steps must be taken to begin the separation," he said in a newspaper interview.

Blue White Future, a relatively new organisation, also argues for "constructive unilateralism", by which it means Israel withdrawing to the security barrier, with voluntary evacuation and compensation for those in settlements beyond. "Once Israel announces it has no sovereignty claims east of the fence, most [settlers] will move westwards," said Orni Petruschka, co-chairman.

Some have even suggested the "cantonisation" of the West Bank. The Palestinian Authority would be given autonomy in five cantons around the main West Bank cities of Ramallah, Jenin, Nablus, Bethlehem and Hebron, with Israeli sovereignty over the rest of the territory.

There are also growing Palestinian voices declaring the end of the two-state model. "The two-state solution died long ago, with Israel's refusal to confront the settlement movement," said Palestinian analyst Diana Butto. "Unless this colonial project is addressed completely, there cannot be two states, only apartheid." The battle now, she said, was for universal rights within the one state that is in de facto existence.

Among those still fighting for a two-state model are European diplomats in Jerusalem who have identified a handful of West Bank and East Jerusalem settlements as "game changers". Significant growth in these places would signal crossing a red line, they say. "There's a year, or 18 months maximum, before it's over," said one.

Molad, a young leftist Israeli thinktank, says it is fighting an "irreversibility thesis". According to director Avner Inbar, "talk of the end of the two-state solution is irresponsible. The two-state solution is not only the best framework, it's the only one that will work. None of the advocates of one state talk of the likely consequences. It would result in dramatic and possibly catastrophic violence."

Barring the unexpected, the most likely course is continuation of the status quo – Netanyahu's preferred option and so, it seems, Republican candidate Mitt Romney's, judging by a recently leaked video. But as many analysts and diplomats point out, the "status quo" in practice means the entrenchment and growth of settlements.

A reinvigorated second-term Obama presidency could change that. In an interview with ABC in July, the president was asked if there was anything he believed he had failed at, that "has you desperate to get that second term to atone for?" There were "a bunch of things that we didn't get done that I think were important," replied Obama. On foreign policy, he said, "I have not been able to move the peace process forwards in the Middle East in the way I wanted".

Faith, as well as time, has been lost. "Obama has learned this is not an issue that will win him any votes. I am not someone who believes a second-term president will act any differently that he did in his first term," said Butto.

According to Dayon, "Obama has learned the limitation of his powers to make change here. President Obama of 2012 will not be the same as President Obama of 2008 because he now realises he cannot deliver."

Back in Ariel, students are hurrying between classes at the start of term. At the Moskowitz School of Communications, named after the US bingo magnate Irving Moskowitz, who has spent millions of dollars funding the settlement enterprise in the West Bank, 24-year-old Adi said she was thrilled at the institution's new university classification. "It will give graduates better status and better job prospects. Yes, of course, we are situated in the middle of a conflict, but a city like Ariel is very valuable to Israel. We cannot give it up."

Down the road in Shiloh, David Rubin dismissed the idea of evacuating any settlements. "We're supposed to hand over our heartland? This is my country, where my roots are, where my history is, where my destiny is, where the Jewish people were born, exiled from and returned to. This community will never be destroyed. There will never be a deal with the Palestinians."