WASHINGTON — If Senator John McCain had an inkling of curiosity how his old buddy Chuck Hagel felt as the senator raked him over the confirmation coals on Thursday, Mr. McCain would get a slight taste an hour later during his own rendezvous with rudeness.

That is when Senator Rand Paul of Kentucky took to the Senate floor to deride Mr. McCain’s opposition to his measure that would punish Egypt as “spurious and really, frankly, absurd,” not the first time Mr. Paul has wielded verbal scythes toward his colleagues.

The willingness of Republicans to skewer one of their own became increasingly apparent on Friday as more and more members of the party peeled away from Mr. Hagel, President Obama’s nominee for secretary of defense, saying they would not vote to confirm him after Mr. Hagel melted like chocolate on a dashboard under combative questioning from Republicans.

Still, Republican senators and aides said that despite a halting performance, Mr. Hagel would probably be confirmed with Democratic votes. A filibuster of his nomination is still possible, a likely first for a cabinet nominee. Aides to Senators John Cornyn of Texas, the No. 2 Republican, and Ted Cruz, a Texas newcomer, said Friday that they had not ruled out procedural roadblocks to stop Mr. Hagel’s nomination.