Some Democrats, including Mr. Schumer, tried to appeal to Mr. Trump early on.

“I told him infrastructure and tax reform should have been the first thing out of the box,” said Senator Joe Manchin III, Democrat of West Virginia, whom both parties expected to be an early ally of Mr. Trump. But, Mr. Manchin said, the president chose a more partisan agenda. “Someone got to him,” he said.

Mr. Manchin spoke with the president early in his administration — leading to speculation that he might even land a job within it — but has since been largely ignored by White House officials and Senator Mitch McConnell of Kentucky, the majority leader, who has mostly iced out Democrats in this Congress.

Mr. Manchin has no interest in the Senate health care bill, which would greatly cut the Medicaid program in his poor, rural state, a concern shared by his Republican counterpart from West Virginia, Shelley Moore Capito. Mr. Manchin has largely voted against Mr. Trump’s agenda and nominees. (He was the one Democrat who voted to confirm Jeff Sessions as attorney general, but that was out of friendship with Mr. Sessions more than fealty to Mr. Trump.)

The country has a long history of senators from the opposite party working to help pass a new president’s agenda. Former Senator Max Baucus, Democrat of Montana, supported President George Bush on a broad trade agreement, and sided with President George W. Bush on a large tax cut and the expansion of a prescription drug benefit for older Americans, infuriating his own party.

“Both Bushes were very deeply experienced, as were their cabinet officials,” Mr. Baucus said in a telephone interview from Paris on Wednesday, noting that the White House had courted him on every measure he ultimately supported. “Jim Baker took the cake,” Mr. Baucus said, referring to George H. W. Bush’s chief of staff, who called him to wheel and deal on the North American Free Trade Agreement. “Donald Trump and his people have no public policy experience, and it shows.”

Congressional leaders, emboldened by the total Republican control of Washington, are now pursuing a partisan agenda largely through methods that require no help from Democrats. Senate committees, where bipartisan bills have historically been forged, are not developing big bills right now, which have been left to leadership teams instead.

Mr. Baucus, who served in leadership roles on the Senate Finance Committee, met with his Republican counterpart, Senator Charles E. Grassley of Iowa, “every Tuesday at 5:30 for 12 years, even if it was just to talk about our kids,” Mr. Baucus said, and that helped pave the way for bipartisan legislation.