The latest snowfall was a bigger story in Washington this week than Tuesday’s private meeting between the estranged president and House speaker — their first in more than a year. Since Barack Obama recently signaled that he has all but given up on legislating with Republicans, and since John Boehner has flat out said thathe can’t trust the president, the assumption in Washington is that the chances for big legislation anytime soon are basically zero, whether the White House breaks out the good china or not.

A clever Washington Post headline summed up the reaction this way: “Obama and Boehner Meet. No Big Deal.”

It probably invites mockery to raise the tattered flag of optimism here, especially among the unbending partisans on either side who would reject any form of compromise that isn’t a total capitulation of the other, and whose attention has already shifted to 2016, when they plan to win the White House and every one of the 535 seats in Congress, thus obviating any need for negotiation.

And yet I’ll offer the dissenting view that this week’s resumption of face-to-face talks could ultimately lead to a lot. In fact, there are several reasons to think that Obama and Boehner could still salvage their relationship enough to reach accord on some major issues, during the next Congress if not before.

First, although this isn’t a new development, both men (probably more than anyone else in their respective parties) badly want some bipartisan deals, or at least one significant breakthrough. Obama has less than three years left in office, and that could well be the limit for Boehner, as well, who has told friends there are other things in life he’d like to do.

As it stands now, Obama’s “paragraph in history,” as he recently put it to the journalist David Remnick, will reflect mostly futility after the first quarter of his tenure. And Boehner’s signature achievement as speaker will be not getting himself deposed. It’s safe to say that neither man sees this as his ideal legacy.

Story continues

Also, while the breakdown of earlier negotiations over a so-called grand bargain, most notably in 2011, led to recrimination at the staff level in both the West Wing and the speaker’s crypt-like Capitol office, enough time has passed now that aides to Obama and Boehner may have a chance to reset the relationship and the negotiating parameters.

Most of the senior aides who took the lead in earlier rounds (including Boehner’s top two negotiators, his former chief of staff Barry Jackson and policy chief Brett Loper, and their counterparts in the White House, the former chief of staff Bill Daley and legislative director Rob Nabors) have moved on to other jobs. In their place, Obama’s new legislative director, Katie Beirne Fallon, and Boehner’s current chief of staff, Mike Sommers, have opened their own direct line of communication.

And despite all the talk about the vast ideological struggle raging in Washington, the simple truth is that on the three issues these aides and their bosses are most likely to find themselves negotiating—immigration, some restructuring of the tax code and maybe even entitlement reform again—the policy differences really aren’t very hard to bridge, if both sides are willing to move even a little from where they’ve been in the past. The real chasm has to do with trust.

More specifically, neither Obama nor Boehner—nor their aides—trust the other side to follow through with any concession that might infuriate their most ideological allies. Boehner sees Obama as unwilling to confront his party’s congressional leaders and interest groups, and he suspects that the president won’t follow through on enforcing key provisions of any deal. Obama doubts that Boehner will risk his speakership to make any deal for which the tea partiers in his caucus will excoriate him, and even if he will, the White House has been given ample reason to doubt that he can deliver the votes needed to pass it.

This trust gap represents a serious impasse to any bipartisan legislation. But when Boehner boldly pushed through a bill earlier this month that raised the nation’s debt limit, he used an intriguing strategy—and one that might signal another path ahead.

In this instance, Boehner found himself in a familiar conundrum; most of his members wanted to raise the debt limit, except for the contingent of several dozen antigovernment conservatives backed by outside agitators like the Club for Growth. The problem, as always, was that a lot of mainline Republicans who wanted the bill were deathly afraid of being challenged in primaries, and so they weren’t willing to vote for anything that the nihilist caucus opposed.

Faced with this problem in the past, Boehner has usually tried to get a bill that would satisfy his hardliners, so that he could keep his majority together. That’s how he ended up shutting down the government last year.

But this time, fearing that Republicans might self-immolate before the midterm elections, Boehner finally did what Obama has wanted him to do for years; he told his tea party contingent to take a walk. The speaker proposed an unconditional lifting of the debt ceiling, but he also told his other members that they could vote against the bill if they needed to.

As a result, the bill passed the House with mainly Democratic support; only 28 of 232 Republicans voted for it. But most of Boehner’s members were fine with that outcome, because they privately supported the bill and considered it good politics for the party nationally, if not in their specific districts. Boehner’s already strained relationship with the tea party crowd, meanwhile, probably suffered lasting damage.

This might suggest a new reality in the House. Obama’s team is skeptical, and perhaps reasonably so, that the strategy Boehner employed to pass the debt-ceiling increase will have larger implications. The feeling at the White House is that it was a desperate gambit to avoid political catastrophe, rather than a new way of doing business.

But if Boehner has now lost the most radical members of his party for good, as seems likely, then he has little impetus to negotiate other deals with their support in mind. And there’s no good reason, then, not to pass the legislation he wants with largely or even mostly Democratic votes, while at the same time retaining as much of a Republican bloc as he can.

When I asked Boehner’s spokesman, Michael Steel, if the same strategy might work on an issue like immigration, where a centrist solution is likely to attract the support of a lot of the Republican caucus but not necessarily all their votes, he chose his words carefully. “We could get to a place on immigration where members want that to happen but won’t vote for it,” he said. “But we’re not there yet.”

It’s true — we’re not at anything close to a pivotal moment and probably won’t be until after this fall’s elections. But that moment is coming, and as Obama and Boehner eye their respective legacies, no one should assume that this week’s meeting is going nowhere. My guess is that the president and the speaker, for all their mutual disdain and disillusionment, will find themselves locked in a room again before long, facing another series of critical choices.

In Washington, things often seem like no big deal, until suddenly they are.