(CNN) Everything in Washington comes down to this: It's House Speaker Nancy Pelosi vs. President Donald Trump.

America's two most powerful leaders came face-to-face Wednesday in the most awkward of meetings. It was the latest twist in a many-layered test of wills that has momentous implications for the nation's future.

Pelosi had a frying-pan-into-the-fire moment when she headed to the White House to talk infrastructure reform after a meeting of her Democratic caucus, which is pulsating with calls for Trump's impeachment

"We believe that the President of the United States is engaged in a cover-up," Pelosi said, setting the stage for tense atmospherics with Trump. Pelosi has been cool to rising demands from her caucus to initiate impeachment proceedings -- and it appears that the party has not yet reached a tipping point on the issue. Multiple sources told CNN that Pelosi instructed her lawmakers not to use calls for impeachment in fundraising pitches.

Trump warmed up for the meeting on infrastructure with congressional leaders with a series of Twitter blasts.

"Everybody, including me, thought that when the 40 Million Dollar Mueller Report was released with No Collusion and No Obstruction (of a crime caused by others), that was the end. But no, the Democrats want to keep it going in an effort to help them in 2020. Bad for the Country!" Trump wrote.

At the White House, the speaker joined another longtime Trump antagonist, Democratic Senate Minority Leader Chuck Schumer of New York, and key committee chairs to discuss the President's b ipartisan $2 trillion infrastructure plan.

It was a momentary truce amid an expanding, multi-front war between Pelosi's House Democrats and the White House, which is fast bringing America to the cusp of a constitutional crisis.

Pelosi's legendary grip on her Democratic troops is facing perhaps its most sig nificant test over her reluctance to swiftly initiate i mpeachment hearings against Trump, even as he mounts a suffocating effort to thwart Democratic investigations.

Those growing calls to start an impeachment inquiry now include House chairmen, such as the head of the Budget Committee Rep. John Yarmuth, who told CNN on Wednesday morning "I think a growing majority of our caucus believes that impeachment is going to be inevitable."

Pelosi's subordinates sent new subpoenas to one of Trump's most trusted confidants -- his former communications director Hope Hicks -- and to Ann Donaldson, McGahn's plugged-in former chief of staff.

And the Presiden t launched an appeal against a federal court ruling on Monday that ordered his accountants to hand over years of financial records to a House committee.

While they are seeking to identify a patch of common ground in the political no man's land, Pelosi and Trump will struggle to conceal their efforts to use ongoing budget negotiations and their showdown over scandals to achieve irreconcilable political goals.

All that Pelosi does -- from her handling of impeachment demands to gambits on health care and social services -- is to position her party for 2020 in the hope of making Trump a one-term president.

Trump, meanwhile, faces one of his biggest domestic tests as President as he tries to shape looming budget and debt cliffs to bolster his reelection and attempts to fulfill campaign promises like building his wall, while he tries to grab back Pelosi's House majority and send her into retirement as he embarks on a second term.

A tense relationship

Given their ceremonial roles, Pelosi and Trump cross paths quite often -- and are usually civil to each other.

But the California Democrat's condescending "clap back" at Trump during his State of the Union address last winter went viral and launched scores of internet memes, a sign of the tension that crackles between them.

And Schumer, Pelosi and Trump clashed during a stunning televised presidential venting se ssion over immigration late last year in the Oval Office.

There is none of the rapport between the speaker and the President that there was -- despite fraught political differences -- when George W. Bush was in the White House. Their bond was on display as they embraced when the body of Bush's father, former President George H.W. Bush, was lying in state in the Capitol in December.

The extraordinary backdrop to Wednesday's talks, a full-blown separation of powers blowup, will complicate the already questionable chances of a rare bipartisan initiative.

Infrastructure improvement is a program both sides want -- not least to lay before their different sets of voters in 2020. But it's an issue that often founders on political divides, as goodwill is drained by unrelated disputes and no one can agree on how to pay for new roads, bridges, railroads and airports.

And in truth, infrastructure may be one of the least important current questions of vital national interest that must somehow be navigated despite the antipathy between Trump and Pelosi.

The decisions the rivals will face in the coming days -- on the budget and the debt ceiling, for instance -- could hardly be more critical. They will reverberate through the economy, test America's good global credit and affect millions of people.

There were some hopeful signs that there may be a path to a budget deal, at least on Tuesday.

Negotiators from the White House and bipartisan congressional leaders met in search of an agreement tha t would set spending levels and suspend the nation's borrowing limit for two years.

Such a deal could stave off $120 billion in automatic spending cuts and cut much of the risk of another government shutdown, after Trump came off second best in the last such showdown.

Senate Majority Leader Mitch McConnell said he hoped a deal could be reached before the end of Tuesday. But a second round of talks broke up without word of a compromise.

"We're working hard on it," Schumer told reporters, saying the talks were "productive."

Still, the acid test of any deal is whether Trump will agree to sign off on it and stick to it -- even though his representatives were in the talks -- following many last-minute reversals by the President.

And while an agreement could build some goodwill, the gravity of the confrontation between the House and the White House over the Russia investigation means it's unlikely to last long.

The impeachment conundrum

Pelosi has said she believes the President is trying to goad her into opening impeachment hearings, figuring that the ensuing political meltdown will help his reelection bid.

She's trying to keep a brake on her party for fear that a futile effort to oust Trump -- due to the GOP majority in the Senate -- will drown out Democratic priorities on health care and economic equality and could spark a backlash.

But she is seeking to use Congress' power to hold Trump to account -- and the court system, as witnessed by Monday's victory -- in order to keep the focus on the President's alleged misdeeds.

"I think the President every day gives grounds for impeachment in terms of his obstruction of justice. You never say, blanketly, I'm not answering any subpoenas," she said last week.

But a growing number of Democrats -- including, for the first time, key members of House leadership -- are demanding the start of an impeachment inquiry. Rank-and-file members, too, are becoming more outspoken.

Democratic Rep. Val Demings of Florida said the evidence in the Mueller report was sufficient for Democrats to take the next, fateful step.

"I believe it's pretty clear that the President made numerous attempts to obstruct justice or obstructed justice," Demings, a member of the House Judiciary Committee, told Jake Tapper on "The Lead."

"And so I believe, based on that information, as I did a month ago, that we have enough to begin those proceedings."

Even some of Pelosi's most loyal committee chairmen seem to be edging closer to an impeachment epiphany.

"I'm getting there," House Oversight Chairman Elijah Cummings, a Maryland Democrat, told CNN's Manu Raju on Tuesday, explaining that he was getting closer to supporting an impeachment inquiry.

Another powerful Democrat, Rep. Adam Schiff of California, who runs the House Intelligence Committee, appears to be heading in a similar direction.

"The case gets stronger the more they stonewall the Congress," Schiff told CNN on Tuesday.

This post has been updated with additional developments Wednesday.