There was always a mismatch between the tea party personality of the new Republican majority in the House and the politician that majority chose to lead them, House Speaker John A. Boehner (R-Ohio). After Thursday night’s dramatic implosion, the country better understands the consequences.

The stunning events that played out Thursday night, as Boehner was forced to pull from the floor and rework the debt-ceiling legislation he had put up for a vote, was both a failure of leadership and a failure by those who wouldn’t follow. But it was perhaps inevitable.

Republicans asked the voters last year to give them the power to help govern the country. Thanks to dissatisfaction with the policies of President Obama and the dismal state of the economy, voters complied.

With that authority awarded through the ballot box came an obligation to recognize both the power they were given and the limits it entailed. Instead, House Republicans have spent the past two weeks debating debt-ceiling proposals that have no possibility of becoming law at this time. What they discovered Thursday night is that they were divided enough internally to scuttle passage of a plan that Boehner had put his prestige behind.

Boehner and other GOP leaders spent Friday picking up the pieces of Thursday’s debacle, and by the end of the day they had emerged with passage of a proposal that had been retailored to meet the demands of the holdouts. The speaker’s fiery speech ending debate brought a standing ovation from his troops.

How much damage the events of the past two days have done to efforts to resolve the current impasse isn’t yet known. Boehner and the Republican Party could suffer well beyond the outcome of this episode if enough of the public judges that they are not governing in the country’s best interests.

The changes Boehner was forced to make to his proposal will make it even more unpalatable in the Senate. Any compromise that comes back will fall that much farther short of what his rebellious colleagues want.

If there is to be a compromise — and the outlines of a plausible agreement were under active discussion on Capitol Hill before the House bill was pulled — it is likely to be one that splits the Republicans in the House far more than they were divided on Thursday night.

When he broke off negotiations with the White House, Boehner took upon himself the responsibility to find a solution to the debt-ceiling deadlock. He turned the president largely into an observer this week, save for a prime-time speech on Monday and another statement delivered Friday morning. In so doing, Boehner heightened the pressure on himself to deliver.

When he pulled out of the White House talks a week ago, Boehner accused the president of not being willing to take yes for an answer in their negotiations. What is ironic, or worrisome, is that he has struggled to persuade his troops that, with the collapse of the grand bargain, they had won the argument — certainly for now at least.

Neither Boehner’s plan for a two-step process to raise the debt ceiling nor the single-step process advanced by Senate Majority Leader Harry Reid (D-Nev.) calls for more taxes. The grand bargain so prized by the president — and seemingly, for a time, by the speaker — seems long gone. But for the tea party faction in the House, that hasn’t been enough to feel satisfied. Their suspicions of Washington run that deep.

Boehner might look back and regret the speech he gave on Wall Street this past spring, when he said any increase in the debt ceiling would have to be matched dollar for dollar with spending cuts. That might have been the price of holding his troops in line as he entered negotiations, but it has tied his hands at a time when some flexibility is desperately needed to resolve the impasse.

Boehner is an old-school Republican politician, once happy on the back benches of the Ohio legislature and long comfortable in the backrooms of power. His troops abhor the very image of that kind of politicking, which might be why it was the speaker who yielded in the late-night bargaining sessions Thursday rather than the holdouts.

Boehner’s hold on power has always been qualified, with House Majority Leader Eric Cantor (R-Va.) constantly on watch and giving voice to the big freshman class that has changed the complexion of the party. As a result, he has struggled to reconcile his desire to make deals with Democrats, something he has always taken pride in, with the no-compromise attitude of those who arrived in January determined to put a stop to the shenanigans they believe Republicans have engaged in over the years.

Though the president’s personal numbers remain soft and should be a cause for concern among Democrats, public opinion on a resolution to the debt and deficit problem continues to side with him. A strong majority believes that the solution should include spending cuts and tax increases. In a recent Washington Post-ABC News poll, many more Americans saw Republicans as the bigger obstacle to a compromise.

In the normal course of politics, a party on the wrong side of public opinion begins to correct its course. In this case, House Republicans are paying attention less to the public at large and more to the views of the tea party activists who helped propel them to power in the fall. They could pay a steep price for that if the public concludes they were responsible for putting the government in default or further damaging the economy.

There is still time for a compromise. Congress can move quickly when it must. If there is an agreement, it will come only through the efforts of Harry Reid and Senate Minority Leader Mitch McConnell (R-Ky.), who like Boehner was often on the wrong side of battles between the tea party and the GOP establishment last year.

McConnell has had little choice but to stand with the speaker as events played out in the House. He also knows what could happen if the public starts blaming Republicans for a breakdown that hurts the already weak economy. Now, as the real negotiations in this unpredictable drama can begin, the stakes for Boehner and his party couldn’t be higher.