A president rarely has as much capital as he does in the first six months, as Mr. Obama realized when he plowed through major legislation like an $830 billion stimulus bill, an expansion of the Children’s Health Insurance Program and legislation to empower women to sue over unequal pay. But Mr. Trump now finds himself like a rookie poker player at the high-stakes table at the Venetian hotel, short on both momentum and chips.

The White House press secretary, Sean Spicer, stepped to the lectern on Tuesday to recite what he framed as a litany of successes for Mr. Trump, but as they say in politics, when you’re explaining, you’re probably losing.

Congressional Republicans made the internal deal that they would endure the embarrassments and foibles of Mr. Trump to get their party’s agenda underway, and now find themselves with roughly 30 days left before the August recess, with only a Supreme Court confirmation to show for it.

In those 30 days, the Senate has promised a vote on a bill to repeal and replace the Affordable Care Act, whether they have a majority or not. The House and Senate are supposed to produce and then pass budget blueprints for the fiscal year that begins Oct. 1, then reconcile their differences and vote again. And the Treasury Department has said members of Congress must raise the government’s statutory borrowing limit before they leave for the summer.

Many Republicans seem leery of continuing to use procedural methods to shut Democrats out of legislation. Already, they have tried to finesse the difficult task of passing health care legislation through the budget rule, devised in 1974 to ease tough votes to control the deficit. They have vowed to use it again to ram through the first thorough rewrite of the tax code since 1986. Now, the Trump administration has raised the idea of using the same method to pass an infrastructure bill — the one Trump proposal that was supposed to have bipartisan appeal — with a simple majority.

“If we can’t do 60 votes on infrastructure, we probably couldn’t do 60 votes on anything,” said Senator Roy Blunt, Republican of Missouri, referring to the minimum number of senators needed these days to pass a bill, and one that would have to include Democrats.

Democrats, and some Republicans, argue that Republicans’ years of opposition cauterized their mind-set toward legislating. “The hard right, which has disproportionate influence in their conference, has meant they are very good at the negative and not so much the positive,” said Senator Chuck Schumer of New York, the Democratic leader.