The House returns on Tuesday.

Mr. Trump is hardly the first president to fight with his party over major policy matters. President Jimmy Carter’s fights with fellow Democrats over nearly everything prompted Senator Edward M. Kennedy to challenge him for the party’s nomination in 1980. President Barack Obama fought with coal-state Democrats who sunk his climate change bill and with war-weary members of his party over whether to launch airstrikes in Syria.

“The general dynamic to get congressional leaders aligned with the White House is often a challenge, but rarely impossible,” said Patrick Griffin, a former aide to Senator Robert C. Byrd of West Virginia and a legislative director during President Bill Clinton’s first term. “This dynamic is only different in that the president is so unpredictable. What should be obvious is not a certainty.”

Counterproductive as his moves may appear, Mr. Trump is clearly eager for a victory, and funding for his wall would be one, at least with his base. His negotiating method appears to be to join the conversation late and pressure Congress via his beloved Twitter account, with references to campaign promises that were always long shots.

“The president is not beholden to the same constituencies as previous Republican presidents,” said Ken Spain, a former spokesman for the National Republican Congressional Committee. “That was a major asset for Trump as a candidate, but from a governing perspective it can lead to competing priorities with the more conventional wing of the party.”

Mr. Spain added, “To the extent the White House and Republicans on Capitol Hill can utilize a hand-in-glove approach, the likelihood for success increases dramatically.”

While many presidents bring advisers from their home state during their first term, they also tend to staff up with people wise to the ways of working with Congress. But like Mr. Carter’s, Mr. Trump’s inner circle is particularly full of close associates who have not spent time in Washington, and have learned the hard way — at the hands of lawmakers, often from their own party — about what is and is not possible.

“They learn Congress is a coequal branch of government,” said former Senator Trent Lott, Republican of Mississippi and a onetime majority leader. “What Congress has to do and the Senate majority leader has to do is say to the president of their own party sometimes is, ‘We appreciate your interest, but we are not going to do that here today.’”