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Chairman Patrick J. Leahy, Vermont Democrat, said he is considering changing Judiciary Committee rules to circumvent Republican opposition.

“If this obstruction continues with respect to judicial nominees, I will be forced to reconsider long-held policies that have upheld the rights of the minority party in this process,” Mr. Leahy said.

Sen. Chuck Grassley of Iowa, the ranking Republican on the committee, said Democrats shouldn’t be surprised.

“The fact of the matter is that given the atmosphere the Democrats created by invoking the nuclear option, nominations are going to be given added scrutiny,” he said.

Each side marshals statistics. Democrats point to the number of vacancies, and Republicans say they have allowed more than twice as many judicial picks to be confirmed during Mr. Obama’s fifth year in office than minority Democrats allowed during President George W. Bush’s fifth year.

In the case of the Mayorkas nomination at Homeland Security, Republicans said it’s the first time the Senate has knowingly confirmed such a high official who is under investigation. They said it’s another ignominious precedent for Mr. Reid, the driving force behind Mr. Mayorkas‘ confirmation.

Mr. Reid questioned the inspector general’s credibility, and the chief of the inspector general’s office resigned just days before the vote to avoid congressional scrutiny and added drama.

“This is all kind of inside-Washington politics,” Mr. Reid said in dismissing the investigation.

The vote was along party lines, 54-41, signaling that Mr. Mayorkas wouldn’t have been cleared if the old filibuster rules were in place.

Sen. Tom Coburn of Oklahoma, the ranking Republican on the Senate Homeland Security Committee, told colleagues he was stunned that Democrats were going ahead with the vote.

He said analysts who researched the record couldn’t find any instances in which a nominee under active investigation had been confirmed.

“It’s never been done before,” he said.

Mr. Coburn said if the review, which he said could take a few more months, cleared Mr. Mayorkas, then he should be confirmed easily.

The senator from Oklahoma also said Mr. Obama was being hypocritical by continuing to push Mr. Mayorkas‘ nomination. When Mr. Obama was in the Senate, Mr. Coburn said, he objected to moving ahead with one of Mr. Bush’s nominees who was under investigation.