Barack Obama begins his first official visit to Israel on Wednesday amid growing warnings among some of its leading supporters in the US that the president needs to act more forcefully to save Israel from itself.

The White House has played down expectations that Obama will put any real effort into pressing Israel toward the creation of a Palestinian state after he was burned by an attempt early in his first term to pressure the prime minister, Binyamin Netanyahu, into halting Israeli settlement construction in the occupied territories.

But there is increasing concern among some of Israel's backers in the US that without White House intervention the much promised two-state solution is doomed – and that will endanger Israel.

Among those sounding the warning is the US secretary of state, John Kerry, who said earlier this year that "the possibility of a two-state solution could shut on everybody and that would be disastrous, in my judgment".

The inclusion of hardline pro-settler ministers in Netanyahu's new government, who are expected to press for the continued expansion of Israel's colonies in the West Bank, has heightened concerns in Washington that physical realities on the ground are making the prospect of a negotiated agreement ever more difficult.

Others have pointed up a recent Hebrew University demographic study, which showed that Jews are now in a minority in the territory covered by Israel, Gaza and the West Bank – suggesting that Israel's democratic and Jewish character are threatened by its reluctance to give up territory to an independent Palestine.

That led David Aaron Miller – a negotiator in efforts by the Clinton administration to broker an Israeli-Palestinian agreement and an adviser on Middle East policy to six US secretaries of state – to advise Obama to "take a quick tour around Israel's demographic neighbourhood" in order to understand the issue that might be most persuasive in pressuring Israeli leaders to take negotiations with the Palestinians seriously.

"Demographic trends mean that Israel can't have it all. It can't be a Jewish state, a democratic state, and a state in control of its whole historical land. It can only have two of its objectives at a time," he wrote in Foreign Policy.

"The demographic imperative probably appeals to Obama, a rational thinker who understands the importance of acting in the present to avoid future catastrophes. He has at least once referred to the demographic realities in his speeches on the Israeli-Palestinian conflict. But the president also knows from his own political choices that getting politicians to take risks now to prevent disasters and gain rewards later isn't so easy."

It is a warning echoed earlier this month by S Daniel Abraham, a US billionaire, confidante of American and Israeli leaders, and founder of the Center for Middle East Peace in Washington, who chided the president for not using his visit to press Israel's leaders to confront the looming "tipping point".

"Obama should realize that Israel's continued presence in the West Bank is an existential threat to its continuity as a democratic, Jewish state — and time is not on Israel's side," he wrote in the Atlantic.

"Right now – not in five or 10 years, but right now – only 50% of the people living in the Jewish state and in the areas under its control are Jews. The dreaded tipping point – which advocates of the two-solution have been warning about for years – has finally arrived."

That is a warning reinforced by an Oscar-nominated documentary, The Gatekeepers – in which former heads of the Israel's internal security organisation, the Shin Bet, warn that the occupation is endangering Israel – which has shaken up the assumptions among some in the Jewish community and among Israel's other supporters in the US.

Martin Indyk, a former US ambassador to Israel and now vice-president of the Brookings Institution, said it is clear there is a growing sense of alarm among some policymakers in the US. But he said it may be misplaced.

"My sense is that this is the view of Secretary Kerry – that there's an urgency to try to not just resume negotiations but to resolve at least some of the critical issues in the conflict because the two-state solution is in danger of cardiac arrest. I think there is an urgency, but I don't actually think that if the window closes it can't be prised open again," he said.

"The simple reason for that is there is no alternative to the two-state solution – except no solution. And no solution for the time being may suit both sides… in preference to the kind of compromises and the hard decisions that have to be made in order to achieve a solution. We are fond of saying, and our leaders are fond of saying, the status quo is not sustainable. But if you go out there on both sides, especially compared to what is going on around them – in Syria to the north and Egypt to the south – the status quo, it's OK."

Indyk said there will not be movement until leaders on both sides are prepared to make hard decisions, and that Obama is probably unwilling to force that after his "searing experience" of dealing with Netanyahu over the Jewish settlements four years ago.

"I think that there is something achievable, and I actually think it's very important. And that is that President Obama has the opportunity to reintroduce himself to the Israeli public. The first time he introduced himself to them was in Cairo, wherein he gave his speech in June 2009, which was, of course, addressed to the Arab world and not to Israel … And (Israelis) got the impression that he wants to distance the United States from Israel in order to curry favour with the Arab world," he said.

"It is hard to imagine that the president himself is going to do much more than make this visit. There are greener pastures that beckon him in Asia, and you can see, from a variety of other actions that he's taken or hasn't taken in the Middle East, that he would rather turn away from this region. John Kerry has exactly the opposite instinct. He wants to engage in the Middle East and, in particular, he wants to take on the Israeli-Palestinian challenge, and it's a high priority for him."

There have also been calls from inside Israel for Obama to take a strong position with Netanyahu. Alon Liel, a former director general of the foreign ministry in Jerusalem and a former Israeli ambassador to South Africa, said last week that Israel's rule over the occupied territory amounts to an "apartheid state" – a once taboo comparison that is increasingly heard in the US.

He called on Obama to remain at home if he does not plan to warn Israelis about the dangers of the looming "apartheid cliff".

"If you, President Obama, intend to come here for a courtesy visit, don't come. We don't need you here for a courtesy visit," Liel told a conference in Jerusalem.

"You cannot come to an area that exhibits signs of apartheid and ignore them. That would simply be an unethical visit. You yourself know full well that Israel is standing at the apartheid cliff. If you don't deal with this topic during your visit, the responsibility will at the end of the process also lie with you."

• This article was amended on 20 March to correct an error, introduced in the editing process, that referred to a Hebrew University demographic study and read: "Jews are now in a minority in the occupied territories". The corrected sentence reads: "Jews are now in a minority in the territory covered by Israel, Gaza and the West Bank".