WASHINGTON (AP) — The terms "billions" and "trillions" are tossed around in the nation's debt ceiling debate. Probably no number, however, is more important than 217.

That's how many votes are needed in the 435-member House, with two vacancies, to pass any measure to raise the nation's debt limit and avert economic convulsions in about two weeks.

Interviews with more than a dozen key players Tuesday suggest it's possible, but not easy.

The Senate, with its competing proposals from the "Gang of Six" and Republican leader Mitch McConnell, has dominated public attention so far. But the GOP-controlled House is the tougher challenge for President Barack Obama and others, who say it would be catastrophic for the nation to breach its borrowing limits and begin defaulting on obligations.

Speaker John Boehner, R-Ohio, has echoed the warning. But he is struggling to lead an unwieldy Republican membership that's heavily influenced by debt-hating tea partyers. And he will need help from the Democratic minority, dominated by liberals following the 2010 elections, which swept away dozens of moderates.

It's a numbers game. And here are the key numbers:

The House has 240 Republicans. But 38 have signed a pledge to oppose any debt ceiling increase unless it is accompanied by a constitutional amendment to balance the budget, which is politically unachievable.

"That's a big number," said Rep. Steven LaTourette, an Ohio veteran with close ties to Boehner. And the GOP "no" vote is almost certain to grow, he said, because many Republican lawmakers will stand pat with Tuesday's House vote for the balanced-budget amendment, a measure sure to die in the Senate.

The danger in the balanced-budget push, LaTourette said, "is that the more conservative among us will say, 'OK, I made my vote, and now I'm not going to make another.' And if that gets up to 40 or 60 or 80, then you've got to go back" and negotiate with House Democrats and the White House.

That could raise new problems.

Several House insiders agreed it's quite possible that at least 80 Republicans will refuse to vote for any debt ceiling increase. If so, at least 57 of the House's 193 Democrats would have to vote aye to raise the debt limit. But many Democrats will find it hard to swallow a Republican-dictated package that no includes no additional taxes, even on the wealthiest Americans.

The goal of 217 assumes that all members actually vote. Getting to that number would represent a remarkable degree of bipartisanship in an era of bitterly partisan divisions. Obama's health care overhaul of 2010, for example, passed without a single Republican vote in the House or Senate.

Boehner's best hope is to mimic an April vote in which 81 Democrats joined 179 Republicans in voting for a budget deal that averted a government shutdown.

The debt-ceiling issue is tougher. It wasn't clear Tuesday how much has changed since last week, when House Majority Leader Eric Cantor, R-Va., said, "Nothing can get through the House right now."

"There's a certain air of uncertainty because it's very hard to quantify the 'hell no' vote," said James Lucier, a political and financial adviser with close ties to congressional Republicans.

Adding to the uncertainty is a growing number of proposals despite a looming deadline, underscored by Tuesday's revived efforts by the Senate's bipartisan Gang of Six.

Their plan would cut the deficit by more than $4 trillion over the next decade, in part by generating $1 trillion in new tax revenue. Those targets are similar to Obama's so-called grand bargain.

Boehner partly embraced Obama's plan before conservative Republicans' complaints forced him to back off, at least for a while.

"I just talked with the speaker and he still would like to get the big deal done," LaTourette said Tuesday. "For all these folks who are nervous politically, he makes the case that it's easier to vote on the big deal than it is on the little deal" or a scaled-down debt-reduction plan.

A $4 trillion plan, LaTourette said, would include several long-sought GOP goals: phased-in trims to Medicare and Social Security, deep cuts in other spending areas, a reduction in tax rates and the elimination of numerous tax loopholes.

But many House conservatives don't trust the Obama administration and the Democratic-controlled Senate to follow through on major tax revisions that can't be hammered out before the debt ceiling deadline arrives.

As for $1 trillion in new tax revenues, House Republicans have taken such a hard line against new taxes that it's highly questionable whether such a proposal could be approved.

In an NBC News-Wall Street Journal poll released Tuesday, 52 percent of Republicans said members of their party should "stick to their positions" rather than compromise in the budget debate.

With Boehner virtually certain to lose dozens of Republicans on any debt-hike vote, Democrats hold substantial leverage. House Minority Leader Nancy Pelosi, D-Calif., said in a floor speech Tuesday there's still time to "come together in a bipartisan way" to approve "a grand bargain."

But she continues to demand items that many Republicans reject, including tax increases on the rich and no significant changes to Social Security and Medicare benefits.