WASHINGTON – Amid talk of a possible compromise, the Senate’s second-most powerful Republican and Democrat each claimed yesterday to have enough support for their side’s position as the chamber neared a showdown over the minority party’s right to block a president’s judicial nominees.

Senate Majority Leader Frist, a Republican of Tennessee, intends this week to call up for a vote the first of the blocked nominees – Texas judge Priscilla Owen and California judge Janice Rogers Brown. Mr. Bush nominated both for federal judgeships during his first term, but they and five others were blocked by Democrats.

Should Democrats move this week to block either Judges Brown or Owen, and Republicans fail to break the filibuster, Dr. Frist then would call for the Senate to vote on whether to ban use of filibusters against judicial nominees.

Both sides said yesterday they had the votes to prevail, even as they acknowledge that several middle-of-the-road Republicans had yet to say publicly how they would vote.

“I haven’t given up on the possibility that we might have 60 votes, including some Democrats who’ve been whispering in our ears that they believe that this ought to be defused,” Senator McConnell, a Republican of Kentucky, the chief GOP vote counter, said on “Fox News Sunday.”

Republicans hold 55 seats in the 100-member Senate. Democrats have 44, plus one Democrat-leaning independent.

Dr. Frist needs a minimum of 50 votes to abolish judicial filibusters. Vice President Cheney would provide the tie-breaking vote in his constitutional role as president of the Senate.

Senator Durbin, of Illinois, the Democrats’ vote counter, said his party was united. He said he also expected to pick up GOP support from some of those who have yet to signal how they would vote.

“We feel that there are at least four Republican senators who feel as we do and we feel that there are several who are making up their minds at the last moment,” Mr. Durbin said.

But Mr. McConnell said that should negotiations fail and the vote to end a filibuster fall short, “I believe we will have the votes” to ban the use of filibusters against nominees for judgeships.

Others seemed to be holding out hope for an 11th-hour compromise.

“I believe that, as reasonable people, as we have in the past in the Senate, we should sit down together and work this out,” Senator McCain, a Republican of Arizona, who has broken with his party on the issue, told ABC’s “This Week.”

But Senator Kennedy, a Democrat of Massachusetts, said on CBS’s “Face the Nation” that Democrats “should not accept a compromise that’s going to silence and muzzle and gag a member of the United States Senate to express their conscience on an issue of a lifetime judge.”