WASHINGTON -- Triggering an unusually personal clash, Democrats threatened Thursday to change Senate rules unilaterally if Republicans block yes-or-no votes on several of President Barack Obama's top-level nominees, including some long in confirmation limbo.

A series of showdown votes was set for next week on seven appointees. But in classic Senate fashion, as the rhetoric grew more intense, the two sides constructed an escape hatch in the form of a rare private meeting set for Monday evening where all 100 senators can seek a compromise out of public view.

Majority Leader Harry Reid, D-Nev., set the day's events in motion with a searing speech accusing Republicans of trying to deny Obama the right to have his team in place. In a chamber where senators routinely refer to one another as "my distinguished friend," he accused the Republican leader, Sen. Mitch McConnell, of failing to live up to his commitments to allow votes on all but the most extraordinary circumstances.

Moments later, McConnell said Reid was misquoting him and at the same time failing to honor his own word not to change the rules of the Senate unilaterally. To do so would be a violation of minority rights, he warned, subject to be repeated by any majority in the future. When the drafters of the Constitution gave the Senate the power of advice and consent on nominations, he said, "I don't think they had in mind sit down and shut up."

In Senate-speak, Reid's comments were a threat to invoke the so-called nuclear option, by changing the rules midway through the year to a mere majority vote. Such changes usually are made when lawmakers first convene after an election and require a two-thirds majority, enough to ensure they are bipartisan.

Ironically, a similar set of circumstances occurred during George W. Bush's presidency, when Democrats blocked yes-or-no votes on several of his judicial nominations. The then-majority leader, Republican Sen. Bill Frist of Tennessee, threatened to change the rules to majority vote, and Democrats protested vehemently.

The crisis passed when a bipartisan group of senators worked out a compromise that led to the confirmation of some of the judges and the rejection of others.

There was little sign of such conciliation on the Senate floor during the day.

When Reid formally called in late afternoon for test votes on the seven, Democrats had arranged for Sen. Elizabeth Warren, D-Mass. to be presiding. Warren was once considered a top candidate to head the Consumer Financial Protection Bureau but faced stiff Republican opposition. She used the resulting prominence to launch a successful run for the Senate.

This time, McConnell said "the guy right over here on my left," referring to Reid, was manufacturing a crisis. If it weren't avoided, he added, Reid is "going to be remembered as the worst leader of the Senate ever."

The seven nominees include Richard Cordray, named to head the Consumer Financial Protection Bureau, whom Reid said was first nominated in July, 2011; and three nominees to the National Labor Relations Board, Richard Griffin and Sharon Block, both appointed in December 2011 and Mark Pearce, whose appointment was made last April. Obama named Griffin and Block as recess appointees, bypassing the Senate, but an appeals court has ruled he overstepped his authority and their tenures are in doubt.

Fred Hochberg, nominated as president of the Export-Import Bank of the United States; Labor Secretary- designate Tom Perez and Gina McCarthy, Obama's pick to head the EPA, are also among the nominations involved. All three were appointed in March.

As the leaders clashed, Sen. Roger Wicker, R-Miss., proposed that Republicans and Democrats meet next week to try and reach a compromise. The session will likely be held in an ornate room where the Senate met before the current chamber was built, an arrangement that permits lawmakers to bar the public and the press.

According to Senate records, the most recent such meeting was in January 2007 - when Reid and McConnell wanted to improve working relations among all 100 senators.