President Trump is getting personally engaged in the talks to end a government shutdown, holding an afternoon meeting at the White House Friday with Senate Minority Leader Charles E. Schumer.

Both Republicans and Democrats have been pushing Mr. Trump to become more active in letting them know his specific demands for an immigration deal, which is the key holdup in shutdown talks, after Democrats said they wouldn’t vote to fund the government without a plan to legalize illegal immigrants in place.

“We had a long and detailed meeting,” Mr. Schumer said as he returned to the Capitol midafternoon. “We made some progress but we still have a good number of disagreements.”

Mr. Schumer has been deeply critical of Mr. Trump’s role in negotiations to this point, calling him “impervious to compromise.”

Mr. Schumer also characterized the president as a bad deal-maker earlier this week.

“He can’t maintain a consistent position. We all know that,” the New York Democrat said. “He accepts bipartisan overture on one day, only to reject them on the next. He makes, and then rescinds, and then remakes demands. He encourages compromise one day only to thwart it the next by saying he’ll only accept a deal that gives him 100 percent of what he wants. That’s not what a great deal-maker does.”

But all sides acknowledge Mr. Trump is the key to negotiations, having made demands about what must be part of any immigration deal — then rejecting a bipartisan plan that at least touched on all four of those areas the president laid out.

On Wednesday Senate Majority Leader Mitch McConnell said he was still trying to see what Mr. Trump would accept.

“I’m looking for something that President Trump supports. And he’s not yet indicated what measure he’s willing to sign,” Mr. McConnell said. “As soon as we figure out what he is for, then I would be convinced that we were not just spinning our wheels going to this issue on the floor, but actually dealing with a bill that has a chance to become law and therefore solve the problem.”

Lawmakers seemed intent on avoiding a shutdown, but without a specific path forward, talk Friday turned to how long a stopgap bill should be.

Rank-and-file Republicans were willing to accept something less than the four-week bill the House already approved, but said Mr. Schumer’s suggestion of four or five days was inadequate.

Sen. Edward Markey, Massachusetts Democrat, said Mr. Trump is the only one who can strike a spending deal to stop a shutdown.

“He needs to get in the room with Chuck and Nancy and Mitch and Paul. Only [the president] can get it done,” Mr. Markey said.

The senator said that he is currently a “no” vote.

The meeting between Mr. Schumer and Mr. Trump had Capitol Hill on pins and needles. Asked if he was worried it was just Mr. Schumer meeting with Mr. Trump, Sen. John Cornyn, Texas Republican, said, “The thought had crossed my mind.”

“Senator Schumer’s position confuses me,” Mr. Cornyn said.

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