Perhaps this is obvious, but Republican strategy on Rep. Paul Ryan’s controversial budget plan represents a classic tipping point scenario — enough so that it could be a case study for Malcolm Gladwell’s next book.

The vote on the proposal in the House last month was unusual in the degree of party unity it displayed. Despite warnings that some provisions of the bill were liable to become unpopular, nearly every Republican in the House voted for it, and the tiny handful who dissented did so mostly for idiosyncratic reasons; the Democrats were unanimously opposed. As several other observers have noted, the vote was more in line with what would be expected in a parliamentary system — where party discipline tends to be strong and parties often vote unanimously on many issues — than with the more individualistic and tactical voting that we are used to in the United States Congress.

Still, the Republicans had a sound strategic rationale for voting the way they did. One of the many problems with the Democrats’ health care overhaul, enacted last year, was that almost from the start, there were fractures within the party over what the bill ought to accomplish and how to go about it. It was no surprise that essentially every undecided voter wound up disliking a bill that initially had plurality support: Republicans opposed the bill from the beginning, while Democrats spent as much time arguing against it as for it. A swing voter would have heard much more about the bill’s faults than its virtues.

If you enforce party discipline on a vote, though, you can, by and large, avoid that problem. That does not necessarily mean that a bill will be popular: sometimes a party concludes that it’s worth taking some short-term risk for longer-term gain, and gets squarely behind a measure that voters do not love. But unity in the party can make a bill less unpopular than it would have been if there were significant internal dissent.

The problem with this approach is that you’re counting on some legislators to take one for the team, and cast a vote against their narrow best interest. Voting for Mr. Ryan’s bill probably did not help many of the 60 or so Republican representatives whose districts were carried by Barack Obama in 2008. Still, if the public regarded the vote as more or less the usual partisan posturing on the budget — Democrats vote one way, Republicans the other — the down side of backing the Ryan plan might have been limited.

Once some Republicans start to defect, though, the public may come to view the bill in a different way. Instead of seeing it as a division between Republicans and Democrats — neither of whom are trusted much on budget issues — voters may instead start to see it as a division between moderate Republicans and extremely conservative ones. Voters who are not steeped in the bill’s particulars may well take that as a signal that it is too extreme, and that the “reasonable” majoritarian position is to oppose the plan.

The bigger problem for the Republicans, though, is a snowball effect: each Republican lawmaker who comes out against the bill makes it a bit less popular — and that in turn increases the incentive for other Republicans to break ranks too. Some Republican House members might be willing to stomach voting for a bill that has the support of 45 percent of the voters in their districts, but if popular support is just 40 percent, or 35 percent, they may throw in the towel. So a feedback loop develops, and one defection begets another.

That’s why many Republicans were apoplectic when, for reasons that are still hard to understand, Newt Gingrich denounced the bill on “Meet the Press,” referring to it as “right-wing social engineering.” Though Mr. Gingrich has since tried to walk back the remark, you can be certain that the sound bite will be revisited ad nauseam by Democratic congressional candidates on the eve of next year’s elections.

More recently, Senator Scott Brown, the Massachusetts Republican who faces an intrinsically tough re-election battle next year despite his strong personal popularity, made a show of coming out against the bill with a long commentary in Politico yesterday. I don’t know why Mr. Brown chose that particular forum; it is among the most important reads of the morning for thought leaders on Capitol Hill, but is less important for the voters who will actually decide his race next year. (For some reason, candidates seem compelled to draw attention to their most challenging decisions — another example is Blanche Lincoln and her health care vote.) Even so, Mr. Brown’s announcement will make some Republican chiefs of staff very nervous.

Furthermore, Republicans have to confront an unhappy set of circumstances this week. The special election in New York’s 26th Congressional District today will be regarded, with some justification but also to a degree that is liable to be exaggerated, as a referendum on Mr. Ryan’s budget plan. Then, on Thursday, Harry Reid may compel the Senate to vote on the bill, where it is all but certain to fail. So far, only three Republican senators — Mr. Brown, Susan Collins of Maine and Rand Paul of Kentucky (because he thinks the bill doesn’t go far enough), have said that they will vote against the bill, but several others from among the 14 who represent states carried by Barack Obama may join them.

Nor will that be the end of the issue: Republican candidates for president in 2012 will be asked to clarify their position. The two leading candidates, Mitt Romney and Tim Pawlenty, have had some nice things to say about Mr. Ryan’s budget plan, but have also left themselves enough wiggle room to revise their positions later.

There are two pieces of good news for Republicans. First, they hold only 10 of the 33 Senate seats that will be contested in 2012, and several of those incumbents are retiring, leaving only a handful who must face the voters next year. Senators whose current terms last until 2014 or 2016 might vote for a bill that they would be nervous about backing if they were up in 2012. Second, since almost all House Republicans have already voted in favor of the measure, they may not gain much by reversing their positions now. It’s one thing to oppose a bill from the outset, quite another to flip-flop; a higher threshold is demanded. Even after Mr. Brown’s election last year made manifest how unpopular the Democrats’ health care bill had become, the Democrats mostly avoided defections from members of Congress who had voted for the bill.

Republican members of Congress are probably past the point where they could hope that their yea vote was noticed more by their supporters than by swing voters. This is among the foremost reasons that control of the House — along with the Senate and the presidency — will probably be in play next year.