Nancy Pelosi hasn’t had very many opportunities to influence policy in the 112th Congress. Republicans have too large a majority, and vote too uniformly on most issues, for Democratic votes in the House to make much difference. Instead, the Democrats’ veto points are in the Senate and in the White House.

But the vote to raise the federal debt limit, which now seems tied inexorably to efforts to reduce the national debt, is one exception. We’ve run through these numbers before, but they’re worth revisiting now that we may be getting closer to a deal.

A vote on a deal is a potential triple whammy for members of Congress. Raising the debt limit, in and of itself, is unpopular. So is cutting or amending popular entitlement programs. The cherry on top are potential tax increases — although since some of the revenue raisers on the table poll reasonably well, that is likely to be more of a problem for Republicans than Democrats.

Perhaps the whole is greater than the sum of the parts for the White House (or perhaps not), which if nothing else would get good press coverage if a grand compromise were struck. But that’s less likely to be true for individual members of Congress.

So rustling up the votes is likely to be challenging — especially for Republicans. I calculate that there are only 106 Republicans, out of 240 total, who reside in safe seats and who are not members of the Tea Party. (The latter group is likely to vote against any compromise on principle.)

After I posted the original analysis, some people objected that it is implausible that John A. Boehner, the speaker of the House, would bring a bill to the floor that a majority of his party’s members were likely to vote against. Maybe so, although Mr. Boehner has a number of unusual or unpalatable options, so I don’t think it can be ruled out.

Suppose, however, that Mr. Boehner were able to get the slimmest possible majority of his conference to vote for the bill. That would require 121 votes. Assuming that members of the Tea Party would not budge, that would require his tapping roughly 15 Republicans whose districts might be vulnerable.

Ah, but there is a potential saving grace: redistricting. It’s unclear whether redistricting will benefit Democrats or Republicans overall. But one thing it almost certainly will do is take some of the Republicans in relatively vulnerable seats and put them in relatively safe ones. My original analysis had not accounted for that. This gets a little tricky, because some of the members who might benefit from redistricting may not know it yet, and since a few will move in the opposite direction.

But this does give Mr. Boehner some extra wiggle room. He might also be able to pick up a few votes from members who are planning to retire but have not announced it yet, or those like Representative Peter T. King of Long Island who come from districts where the financial sector is a major employer and thus would have a special incentive to keep the markets happy.

Still, even if Mr. Boehner gets his 121 votes, he’d still need help from 96 Democrats for the bill to pass. Almost certain to be off the table are the votes of the 26 Democrats who I calculate are still in vulnerable districts: having weathered 2010’s perfect storm, why would they rock the boat now? That leaves 166 Democrats to pick from.

But many of those Democrats are liberals. About 80 of them, in fact, are members of the Congressional Progressive Caucus, the most liberal caucus in the Congress. At a bare minimum, about a dozen of those Democrats would have to come along. And potentially quite a few more if the deal also lost some votes among moderate Democrats or if Mr. Boehner proceeded despite not having a majority of his own caucus.

Hence Ms. Pelosi, a former member of the Congressional Progressive Caucus, and its current co-chairs, Representatives Raúl M. Grijalva of Arizona and Keith Ellison of Minnesota, are big players in the negotiation. If they were to whip votes against a deal, it would have a lot of trouble passing.

True, the Congressional Progressive Caucus is not known to be as disciplined as other constituencies in the Congress. And the White House would be working the other end of the phones, trying to cajole or threaten them into a yea vote.

Nevertheless, as you read accounts of the various proposals that are being floated, keep in mind that the views of liberal Democrats are far more than a token issue. That is why, for instance, I thought yesterday’s rumor — tax loopholes that benefit the wealthy would be closed in exchange for temporary cuts to the payroll tax — was more plausible than today’s, which is of a bigger deal that would include changes to programs like Social Security.

The payroll tax cut could be a winner all-around. It’s something most liberal Democrats would like, particularly if it comes on the employee side rather than the employer side or if it is specifically tied to job creation. It is one of the few vehicles available to Mr. Obama to provide for economic stimulus. And, given that the accounting in any deal is likely to be fuzzy, it might give Republicans some cover to say they had voted for tax reform rather than a net tax increase.

It would also mean less deficit reduction than there otherwise would be. But given the diverse constituencies that need to come together to get a deal done, perhaps a smaller deal is more likely than a bigger one.