In remarks on the Senate floor after his meeting with Obama and House Minority Leader Nancy Pelosi (D-Calif.), Reid took a shot at Senate Minority Leader Mitch McConnell (R-Ky.) and House Speaker John Boehner (R-Ohio), who declared at a joint news conference earlier Saturday that they were “confident and optimistic” that a debt deal would be reached in the “very near future.”

“The speaker and the majority leader should know that merely saying you have an agreement in front of the television cameras doesn’t make it so,” Reid said, accusing McConnell and Boehner of “holding meaningless press conferences.”

“The Republican leader says he’s engaged,” Reid continued. “Fortunately, members of his caucus, at least as far as I’m concerned, are more engaged than he is. There are meaningful talks going on with some of his members with my senators.”

Reid’s remarks were the latest sign that Democratic leaders were continuing to focus their efforts on the Republican rank-and-file in the Senate, rather than on leader-to-leader negotiations, in the hope of securing enough GOP support to send a debt-limit compromise to the House before Tuesday’s deadline.

Tensions between Reid and McConnell have been inflamed amid an impasse over Senate procedure: Reid had preferred for his debt-ceiling measure to come up for a vote Friday night with a majority-vote threshold. But Senate Republicans made a bid to block the move, postponing a vote until 1 a.m. Sunday at the earliest and imposing a 60-vote threshold for passage.

On the floor Saturday, Reid charged that Republicans were filibustering the measure, calling the move “unconscionable” and quipping that “you can put lipstick on it, a nice suit, even a skirt sometimes; it’s still a filibuster.”

McConnell responded by arguing that it was Reid who has declined to move forward on his own bill, blaming the “reluctance on the part of the majority to have a vote on a measure they favor, which we’ve been prepared to vote on since last night.”

In a rare, contentious back-and-forth with McConnell on the Senate floor, with senators of both parties looking on, Reid offered to visit the White House with McConnell and called the Kentucky Republican “my friend – and he is my friend, the Republican leader.”

“But I say, as respectfully as I can to my friend, the senior senator from Kentucky, the process has not been moved forward during this day,” Reid said.

McConnell – who had resumed talks with Obama and Vice President Biden earlier Saturday — then rose and took a dig at Reid.

“I actually cut short a conversation with the vice president to come out here for this important vote on a live quorum,” he said, referring to the procedural vote that Reid had called Saturday afternoon to ensure that all senators were present in the chamber.

“The only way that we’re going to get an agreement before Tuesday is to have an agreement with the president of the United States. ... And I’m more optimistic than my friend the majority leader,” McConnell said. “We’ve both talked to the president today; I talked to the vice president several times. I think we’ve got a chance of getting there.”

Ultimately, McConnell said, leaders needed to be in the position where they could “come back here and say we think we’ve reached the framework of an agreement that we can present to our members and be briefing our members.”

The tension of the moment was evident in comments that were picked up by a hot mic as Sen. Charles Schumer (D-N.Y.), who was presiding over the chamber during the back-and-forth, turned to speak to someone to his side after McConnell yielded his time.

“I’m glad you’re here,” Schumer was overheard saying. “We need all the help we can get.”