What the country is watching is a breakdown in governing that could be as corrosive to the political system as the possible financial default looming could be to the economy.

Even before Friday’s collapse in the debt talks, public dissatisfaction with Washington was on the rise. The impasse threatens a further deterioration in public confidence.

There is great disagreement in Washington over the meaning of last year’s midterm elections, but it’s almost certain that most Americans did not vote for the kind of paralysis that surrounds the negotiations over the terms of raising the debt ceiling.

Americans voted for, or got, divided government because the public doesn’t fully trust either party with the reins of power. That means the only way out of this problem is through compromise, or what one administration official called “bipartisanship by necessity,” not by choice.

Up until now, enough lawmakers haven’t been ready to accept that in order for a deal to be struck. So the clock ticks.

The nation’s leaders tried again Saturday to return to regular order after an extraordinary spectacle Friday night, when negotiations over debt and deficits gave way to acrimony and recriminations between President Obama and House Speaker John A. Boehner (R-Ohio). They have little time to repair the damage.

Friday’s dueling news conferences between Obama and Boehner were compelling as political theater. They were more revealing for what they said about why the talks have gone from impasse to near-agreement to collapse more than once over a period of weeks.

The president and congressional leaders of both parties are trying to resolve historic differences over taxes and entitlements. No one should have thought it would be easy.

Republican opposition to tax increases is an article of faith for the party, but many GOP lawmakers, particularly the freshman who came in with the support of the tea party movement, are more rigidly opposed than ever. Similarly, many Democrats, who have won elections attacking Republicans over Social Security and Medicare, remain strongly opposed to cuts in those programs.

Arguments over taxes and entitlements have animated budget fights going back decades. In most cases, through compromise, the two sides resolved their differences, at least for a time. That happened in the 1980s and the 1990s. But now, in a period of partisanship as intense as it has been in many years, the efforts to resolve the current impasse have stretched the system to the limit.

The latest breakdown in negotiations put the country on a collision course with economic chaos, which could begin soon after the Aug. 2 deadline, which is when the Treasury Department says the government will no longer have the authority to borrow money.

Negotiators have just days to show progress, with the onus on the speaker to show that he can cajole his colleagues into accepting a plan that can pass the Senate.

Both sides know it and Obama and Boehner said again that they are determined to avoid default. They met in the White House Cabinet Room on Saturday morning, along with Vice President Biden and the other top leaders in Congress from both parties. The meeting lasted less than an hour.

Neither side is blameless for the current state of the negotiations, but it’s clear the president is closer to having public opinion on his side when it comes to the terms of an agreement. But the public is more closely divided on the question of whom they would blame for an ultimate failure.

Boehner on Friday accused Obama of moving the goal post on taxes, and said dealing with the White House was “like dealing with a bowl of Jell-O.” Obama said Boehner had walked away from “an extraordinarily fair deal” that, if anything, was “unbalanced in the direction of not enough revenue.”

Obama is correct in saying that it was Boehner who walked away, for a second time, from a comprehensive deal that included significant spending cuts, including entitlement programs such as Medicare, that might have put the country on a sound and sustained fiscal footing. Republicans also were asking for more than they could have expected by including the possible elimination of the individual mandate in the new health-care law if the targets in the agreement were not met.

Boehner is correct that Obama called a late audible by asking the speaker to accept a 50 percent increase in the amount of new revenue (read: taxes) in the package, from $800 billion to $1.2 billion. Obama must have known that getting House Republicans to accept $800 billion in new revenues, no matter how it was couched, would be difficult.

That he asked to increase the amount of revenue he wanted showed Obama’s sensitivity to his base, which grew restless late in the week as reports of a possible deal that included mostly spending cuts trickled out, which reflects the worry among many liberal Democrats that the president is prepared to give too much ground on spending cuts and entitlements just to get a deal.

But it’s clear that House Republicans are the principal obstacle to any grand bargain that includes substantial new revenue. Their rigid opposition runs contrary to public opinion, which shows that a majority of the country believes that a deficit-reduction package should include both spending cuts and new taxes.

The freshman Republicans came to Washington determined to cut spending and not raise taxes. They also came with the attitude that past Republican Congresses had been too compliant and too willing to make compromises that in fact boosted spending. They have an aversion to compromise that is as strong as their opposition to taxes.

Republicans have gained more than the freshman House members have acknowledged since the midterm elections. Obama’s willingness to accept the kind of spending cuts on the table shows how much he has moved in the past year.

All of this goes back to how politicians read the election returns. When Obama was elected in 2008, one of the things he had to decide was how much he owed his election to a rejection of President Bush and how much it reflected an embrace of a progressive agenda championed by the Democrats.

Was the 2010 election a rejection of the direction Obama had charted and the results he had produced during his first two years in office? Almost certainly it was. But was it a full embrace of the tea party agenda, as many new Republicans now claim? There’s little evidence of that from the election returns. Republicans made historic gains in the House, but fell short of capturing the Senate.

The country has been through repeated wave elections in which one party or the other has made major gains. The outcomes reflect unhappiness with those in power and dissatisfaction with the state of the economy and the country more than the affirmation of the winners’ agenda.

There is a tendency for politicians, when they are unable to resolve their differences, to say they will take the debate to the country in the next election. That’s what elections are about: big debates over big issues.

But recent elections have not fully resolved the differences, and no one should expect the next one can either. That leaves it to those in office to govern. Only real leadership and real compromise can resolve the way out of this crisis.