WASHINGTON — The Senate inched closer to an eleventh-hour deal late Monday night in a bid to avert an unprecedented maneuver to change the chamber’s rules governing presidential appointees, with nearly all 100 senators spending more than three hours huddled in a rare bipartisan, closed-door caucus.
Rank-and-file senators came out of the meeting reporting progress on the confirmation prospects of President Obama’s selections to head low-profile but influential agencies. Majority Leader Harry Reid, Democrat of Nevada, echoed that sentiment but said no resolution had been reached, leaving in place a critical 10 a.m. Tuesday vote that would set up the historic clash over changing the Senate rules on a raw party-line vote so that Cabinet- and agency-level nominees could be confirmed without having to overcome a filibuster.
Republicans have threatened to retaliate on a host of other legislative matters, creating the possibility that the already toxic tensions in the chamber would hit new heights because of the move that some call ‘‘the nuclear option.’’
Invoking the spirit of early-19th-century deals that delayed the onset of the Civil War, senators met in the Old Senate Chamber, which until 1859 served as the meeting room for such key pacts as the Missouri Compromise of 1820.
‘‘There’s no deal but there’s a much better understanding,’’ said Senator Jay Rockefeller, Democrat of West Virginia, one of his party’s most senior senators. Rockefeller said there was a framework for a possible deal before the showdown votes on Obama’s current picks to run the National Labor Relations Board, or NLRB, and the Consumer Financial Protection Bureau.
Some exited more grim, including Senator John McCain, an Arizona Republican, who spent the previous week in shuttle diplomacy with Reid, Minority Leader Mitch McConnell, Republican of Kentucky, and the White House.
Asked whether Reid had come around, McCain said simply: ‘‘Yes, sort of.’’ He said the talks were now firmly between Reid and McConnell, predicting a long night ahead.
McConnell did not speak after the meeting, issuing a statement declaring ‘‘a clear bipartisan majority’’ supported finding a solution.
Only two of the 100 senators missed the marathon meeting, because of personal commitments, and roughly three dozen senators spoke during the closed-door session. ‘‘I think everybody in there came away with a better appreciation for how the other side feels,’’ Republican Senator Jeff Flake of Arizona, a freshman who sat alongside two Democrats, said afterward.
At the outset, Reid remained defiant Monday, saying that Republicans can avoid a showdown by backing off threats to block seven nominees slated for consideration.
‘‘I love the Senate, but right now the Senate is broken and needs to be fixed. It’s time for course correction,’’ Reid said at the Center for American Progress, a think tank closely aligned with the Obama administration and Democrats.
White House officials said the president had played a behind-the-scenes role in the messy procedural fight, adding that Obama supported Reid in whatever decision he made. At Reid’s urging, Obama has made calls to wavering senators asking them to back Reid if he makes the move.
The dispute centers on Republican treatment of Obama’s nominees, particularly selections for the NLRB, the new finanical bureau, and a couple of Cabinet posts. Republicans, holding 45 seats and enough to filibuster any nominee, have been refusing to confirm the selections for the NLRB and the bureau because they were given interim appointments by Obama that have since been ruled unconstitutional by federal appellate courts. The case is heading for a Supreme Court ruling likely next year.