ALBANY – Senate Republicans on Tuesday cooled their usual efforts to get along with Gov. Andrew M. Cuomo, at least for a day, opposing his selection of a Hispanic woman to the state’s highest court in the morning and, by the afternoon, accusing him of breaking his no-tax-hike pledge.

The Republicans, who partly control the State Senate and have been among the Democratic governor’s most loyal allies in the last two years, said Tuesday that Cuomo is trying to increase taxes by $3 billion in the next five years by extending a surcharge on consumers’ utility bills across the state.

“I think it’s a new tax,” Senate co-leader Dean G. Skelos, a Nassau County Republican, said of the budget plan by Cuomo to keep the surcharge in place beyond its scheduled expiration in March 2014. He called the governor’s plan “counterproductive to job-creation” efforts.

Republicans, joined by groups representing small and big businesses, farmers and senior citizens, vowed to try to beat back the Cuomo tax plan in upcoming budget talks. Sen. George D. Maziarz, a Newfane Republican, called the utility surcharge a “gimmick to fill a hole in the budget.”

A Cuomo administration official said, “We don’t like 18-A [the utility surcharge], either, and we’re happy to sit down and work with the Republicans to find a way to replace that revenue.”

Earlier in the day, in a rare rebuke of a governor’s nominee, Senate Republicans on the Judiciary Committee voted against Cuomo’s choice of a Hispanic woman to the state’s highest court.

The nomination of Jenny Rivera, a law professor, to the Court of Appeals will still go to the Senate floor Monday for a full vote. She is expected to be confirmed, even though she did not have the support of a majority of Senate Judiciary Committee members.

Monday, Rivera faced an unusually tense, five-hour nomination hearing before the judiciary panel. Tuesday morning, with Rivera not present, Republicans as a group, including Sen. Michael H. Ranzenhofer of Erie County, voted either no or “without recommendation” to send Rivera’s nomination to the floor.

In the end, she was backed by 11 senators; three Republicans who voted “without recommendation” legally end up counting as votes that still send her nomination to the floor. Eight Senate Republicans voted no, and there was a member absent from the session.

Republican critics said Rivera, a professor at City University of New York School of Law who served as a civil rights division head under Cuomo when he was the state attorney general, does not have the wide range of legal experience needed to join the Court of Appeals.

Sen. John A. DeFrancisco, a Syracuse Republican, said that he understands that Cuomo wants to have a Hispanic judge on the court and that he would welcome the opportunity to vote for a “qualified” Hispanic nominee.

“We have to have the most qualified person we can get for this position. This candidate is not that candidate,” DeFrancisco said.

Gubernatorial nominees to agencies, boards and courts rarely get the kind of public pushback that Rivera has seen from Senate Republicans in the last two days.

Democrats said Rivera is qualified to serve, and they pointed to judges over the years who had no judicial backgrounds before joining the Court of Appeals.

Sen. Ruth Hassell-Thompson, a Westchester County Democrat, said Republicans “attacked” Rivera during Monday’s hearing and “interrogated” her background and education. “How dare we. We should be ashamed,” Hassell-Thompson told Republicans.

“If this body rejects Professor Jenny Rivera for this position, I believe it to be an offense to the struggle of women, for women seeking qualified employment opportunities. It’s an insult to the diversity and aspirations of Hispanic-Americans everywhere,” she said, adding that a rejection of the Rivera nomination would be “a slap in the face of the governor.”

But Senate Judiciary Committee Chairman John J. Bonacic, a Mid-Hudson Valley Republican, said the seven-member high court makes “decisions that will affect New Yorkers for generations to come.”

Bonacic said he is concerned about what he called the “social engineering” of the court’s selections along racial and gender lines. “I don’t subscribe to that,” he said, noting that the court’s importance requires the best-qualified judges.