The House yesterday approved the Republicans’ debt limit extension. It was a tough vote…I was going to say for Republicans, but it’s probably a tough vote for a lot of Democrats, too. Not so much because of the junk the GOP tacked on, but because raising the debt limit is never popular, even when you call it “suspending” the debt limit.

The vote also demonstrated something important to remember about voting on the House (and Senate) floor: all sorts of things go into final votes.

So: Dave Weigel tweeted after it, “33 R “nay” votes. Without Obama endorsement and D votes this would have gone down.”

Maybe. On the first half of it, certainly; without a presidential signature at the end of the path, there’s no reason for Republicans to bring this to a vote in the first place.

But I wouldn’t be so sure about the rest of it. I took some notes (well, I tweeted them) during the vote, and here’s what happened. It was a five minute vote, and Republicans voted rapidly, and at first voted solidly for the measure. Democrats held back their votes, with those who voted against it mostly voting no. It thereby reached…aw, I didn’t take really good notes, but when it reached a winning number Republicans supported it at 199/9 while Democrats opposed it by something like 19/49. After that point, Democrats split fairly evenly but with somewhat more of them voting yes, while Republicans went from 199/9 to…well, I had 200/32, but I’ll trust that Weigel was correct on the nays, so 199/33.

The question is what happens if Democrats had all voted no. My guess? Boehner probably had the votes, if he needed them. Almost certainly if he needed just a handful more, but perhaps if he needed to supply all of them. Indeed, I’m not certain, but I think that there were at least two yes-to-no switches among Republicans along the way, and perhaps more. Now, those could have been people who accidentally pressed the wrong button…but they also might have been Members who told the leadership they would be there only if needed.

Now, given that Barack Obama and Senate Democrats had already signaled that they would go along with the not-quite-clean-extension that the Republicans had concocted, it’s hardly a surprise that quite a few House Democrats were willing to vote for it. And remember — that’s gong to be true anything intended to actually get enacted into law comes to the House floor. So there’s a fair among of gamesmanship going on with the Democrats, almost all of whom probably wanted the thing to pass even though over 100 wound up voting against it.

And the thing is: no one says (at least not on the record) that their vote was available if needed, but they were happy not to have to vote for that necessary measure that they just voted against. Not only would that ruin the gain of being on record the other way, but no one wants to be seen as the Speaker’s lackey. Nor can we believe the leadership when they claim vote counts.

So, really, we have no certain way of knowing whether Republicans had the votes on this one if they had to do it alone. But I’d bet they had more than the 199 they got.

[Cross-posted at A plain blog about politics]

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Jonathan Bernstein is a political scientist who writes about American politics, especially the presidency, Congress, parties, and elections.