For much of the political establishment, there was a great deal of relief after the debt-ceiling agreement was reached yesterday. There is, however, a nagging question: can it pass?

In the Senate, the votes appear to be in place. ABC News published an estimate this afternoon pointing to passage “with 70-plus votes,” with only 11 Republicans firmly against the measure. The strongest opponents, from the right or left, could conceivably delay a final vote, but barring an unexpected shift, the outcome in the upper chamber isn’t really in doubt.

And then there’s the House. The lower chamber will vote first, probably taking up the bill around 7 p.m. eastern.

Congressional leaders are urgently trying to secure the votes to pass the bipartisan debt limit deal as the House prepares for a critical Monday evening vote.

House Majority Leader Eric Cantor (R-Va.) predicted passage with a majority of the GOP conference behind the deal.

“Working closely with (the whip) and the Speaker, I think we are going to get there,” Cantor said.

That’s fine, of course, but Cantor and other House GOP leaders said the same thing last week, shortly before realizing they didn’t have as many votes as they’d hoped.

Indeed, Republicans are said to be “feeling optimistic that they have the votes for passage,” but given recent events, I’d like to think their optimism wouldn’t be taken at face value.

As of about 15 minutes ago, The Hill‘s vote count showed 45 likely supporters and 25 likely opponents, with the vast majority of members not yet expressing an opinion publicly.

Many of the opponents are on the far-right, which is a reminder that Speaker Boehner will, as expected, need Democratic votes to get this over the finish line. Nancy Pelosi is not exactly feeling inclined to save Boehner’s butt, and the Democratic leadership will not whip this vote, telling members they should follow their own “conscience.”

That’s not what GOP leaders hoped to hear. According to House Minority Whip Steny Hoyer (D-Md.), the deal will need at least 150 Republican votes to pass. Given that the caucus has 240 members, that means Boehner could lose 90 of his own members, and still pass the bill without 70 or so House Dems.

That seems likely, and the odds are in the bill’s favor at this point, but no one should underestimate just how little House Democrats like this package. Given the limited timeframe — members are well aware of tomorrow’s deadline — the pressure to pass the bill will be obvious, but this probably won’t be easy.

For now, there are no reports of party leaders in either caucus scurrying around the Hill, twisting arms and/or pleading for additional votes, which suggests the votes will be there. But no one should take the outcome for granted.

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Steve Benen

Follow Steve on Twitter @stevebenen. Steve Benen is a producer at MSNBC's The Rachel Maddow Show. He was the principal contributor to the Washington Monthly's Political Animal blog from August 2008 until January 2012.