WASHINGTON — A showdown looming, Republicans and Democrats struggled without success Monday night in marathon, closed-door talks to resolve the fate of several of President Barack Obama’s stalled appointees, a dispute that threatened what little bipartisan cooperation remains in the Senate.

Emerging from the session in the ornate Old Senate Chamber — where the public and media were barred — lawmakers from both parties reported progress toward a compromise and said the party leaders would continue talks into the night.

“We’ve had a very good conversation,” said Majority Leader Harry Reid, D-Nev. Yet he gave no indication whether he planned to seek a delay in a series of roll calls planned for morning on confirmation of seven presidential appointees whom Republicans have so far blocked from receiving yes-or-no votes.

Don Stewart, a spokesman for Republican leader Mitch McConnell of Kentucky, said: “A clear bipartisan majority in the meeting believed the leaders ought to find a solution. And discussions will continue.”

Reid insisted in advance that Republicans permit yes-or-no confirmation votes on all seven of the nominees at issue. If they won’t, he declared in a morning speech before the Center for American Progress, Democrats will change the Senate’s rules to strip them of their ability to delay.

The group of nominees includes Obama’s picks to head the Labor Department, the Environmental Protection Agency and the Export-Import Bank. But most of the controversy has surrounded three appointments to the National Labor Relations Board and a head for the newly created Consumer Finance Protection Bureau. Three of the seven nominees were originally named in 2011.

While there were numerous reports of progress toward a compromise in the closed-door meeting, Reid’s pointed observation that votes were still planned for morning had the effect of keeping pressure on Republicans to give ground.

Nearly all 100 senators attended what amounted to an off-the-record session in the chamber where the Senate debated slavery and other momentous issues of the 19th century. In a reference to history, Sen. Lindsey Graham, R-S.C, prompted laughter when he said that the last time a senator from his state spoke in the room, “the Union dissolved.”

Senators in both parties said the session had been candid and even overdue in an institution where gridlock and acrimony have increasingly become the order of the day. Sen. Roger Wicker, R-Miss., who proposed the meeting last week, said afterward, “I think there’s an opportunity to work things out.”