Last year, the Obama administration urged Israel and Arab players in the region to take several interim steps that might create enough confidence to bring Israelis and Palestinians back to the negotiating table.

For lack of sufficient step-taking by all sides, it didn’t work.

Rather than regroup and suggest another series of steps – because that’s how progress in the Middle East tends to move, incrementally – the administration is now looking to take a giant leap forward.

It wants to advance to such “final status” issues as defining the borders of a Palestinian state and agreeing on the role of Jerusalem, which Israelis and Palestinians both claim as their own.

It’s a hugely ambitious strategy, and commensurately, the risk of failure is great. But it also shows a welcome dedication and a renewed push from the administration, without which this seemingly intractable problem can’t be solved.

Bill Clinton also tried to wrap up final-status issues in one big package when he brought the two sides together at Camp David. He failed. George W. Bush, in his Annapolis process, took a more incremental approach. He also failed. Both presidential attempts were followed by renewed violence in the region. Hopes raised; hopes dashed.

One wonders how this will be any different, especially with half of the Palestinian government – the militant Islamist group Hamas, which rules in the Gaza Strip – on the sidelines. How can one negotiate the final shape of a Palestinian state with only a partial representation of the Palestinian people, i.e., Mahmoud Abbas, on behalf of the secular Fatah movement in the West Bank?

The president’s special envoy to the Middle East, former Sen. George Mitchell, suggests an answer. In an interview with PBS host Charlie Rose last week, Mr. Mitchell referred back to his successful experience negotiating the Northern Ireland peace accords in the 1990s.

Negotiations lasted 22 months, he said; for the first 16 of them, Sinn Fein – the political wing of the terrorist Irish Republican Army – did not participate. Sinn Fein only joined the talks after it renounced violence and agreed to abide by a set of democratic principles.

Like Sinn Fein, Hamas will turn around once it sees how the negotiations are going – specifically, once it sees a state shaping up along the pre-1967 borders (Israel took the West Bank and Gaza in the 1967 Mideast war). This, at least, is the hope of those who support the administration’s leap-forward strategy.

Mitchell pointed out another reason why the strategy could work: timing. Presidents Clinton and Bush gave a big push toward peace very late in their administrations. President Obama began 48 hours after taking office, Mitchell quipped. Indeed, one president who started early – Jimmy Carter – sealed the historic Israeli-Egyptian peace accord in his second year in office.

The Obama team suggests that by reaching for an agreement on borders (where there is substantial understanding) and Jerusalem (which is far more contentious), the parties can circumvent the roadblock that’s in the way of talks: Jewish settlements. Borders and Jerusalem would, by necessity, solve that problem.

But Mr. Abbas insists he won’t resume negotiations – which is the immediate aim of the administration – until the Israelis completely freeze settlement building. And Israeli leader Benjamin Netanyahu insists Jerusalem is not negotiable.

That would seem to leave the administration’s fast-forward strategy stuck on pause. But Mitchell is calmly optimistic. Northern Ireland taught him that a negotiator takes neither the first “no” nor the 100th as the final answer.

Remember, he says, that the basic demands of both sides are mutually reinforcing. Palestinians want a state. Israel wants security. Neither party can reach its own objective until it meets the other’s.

May Israelis and Palestinians be spared hearing “no” a thousand times until they get to “yes.”