Senate Republicans have a thorny dilemma regarding President Barack Obama’s nomination of Thomas E. Perez as Labor secretary, especially now that the GOP apparatus has begun to redouble its efforts to reach out to minorities.

If Republicans block Perez, they risk undercutting the Republican National Committee’s brand-new diversity push and getting mired in fights over voting rights and immigration. But if they allow his nomination to go through, they risk blowback from their base. Conservative radio host Rush Limbaugh likened Perez to Hugo Chavez after Obama nominated him Monday. Sen. David Vitter, R-La., quickly announced he’s putting a hold on the pick, and Sen. Charles E. Grassley, R-Iowa, indicated Monday that he may join Vitter.

Don’t think the White House hasn’t noticed.

“The way the far right is reacting to the Perez nom is likely to be included in the paperback version of the RNC report,” tweeted Dan Pfeiffer, a senior adviser to the president. Pfeiffer was referring to the RNC’s 2012 election post-mortem report, released Monday, in which the party argues it needs to do a better job of reaching out to minority voters.

But despite Vitter’s opening salvo, GOP aides told CQ Roll Call it’s too early to tell how tough a fight Perez will face. Much will depend on how he performs in his confirmation hearing. Perez has already been confirmed once, by a 72-22 vote in 2009, when Democrats had a supermajority.

Perez, the assistant attorney general in charge of civil rights laws, is the only Latino Cabinet nominee so far this term, and he has strong support from unions and Hispanic advocacy organizations. The Harvard-trained lawyer and former staffer to the late Sen. Edward M. Kennedy, D-Mass., is whip-smart, politically adept and a committed liberal.

It’s that last part, including Perez’s long advocacy of rights for illegal immigrants and support for new laws mandating higher wages, that has drawn intense fire from the right. Perez’s use of the Voting Rights Act to fight voter identification laws has been strongly opposed by the GOP, and he has faced criticism over his testimony in an investigation of the politicizing of the civil rights division of the Justice Department.

Vitter vowed to hold up Perez’s nomination until the Justice Department answers his 2011 letter challenging the department’s voting rights suit against Louisiana and what Vitter said was nonexistent enforcement of requirements that states purge ineligible voters from the rolls.

“Thomas Perez’s record should be met with great suspicion by my colleagues for his spotty work related to the New Black Panther case, but Louisianians most certainly should have cause for concern about this nomination,” Vitter said. “Perez was greatly involved in the DOJ’s partisan full court press to pressure Louisiana’s Secretary of State to only enforce one side of the law — the side that specifically benefits the politics of the president and his administration at the expense of identity security of each and every Louisianian on the voter rolls.”

Sen. Jeff Sessions, R-Ala., delivered perhaps the harshest criticism of Perez, focusing on his past advocacy for illegal immigrants as president of the board of Casa de Maryland.

“Mr. Perez has aggressively sought ways to allow the hiring of more illegal workers,” Sessions said. “By nominating Mr. Perez to this important post, the president has placed his drive to promote his flawed immigration policies over the needs of the millions of unemployed Americans.”

Democrats are convinced such arguments will simply widen their advantage with Latino voters.

“Despite the fact that Republicans are pledging to reach out to the Hispanic community, they still don’t get it,” said Jim Manley, who used to work with Perez on Kennedy’s staff. For the comments to come out “on the same day that the RNC is pledging to retool their image is just kind of funny,” said the former spokesman for Senate Majority Leader Harry Reid.

Perez also faces a congressional investigation into his role in getting St. Paul, Minn., to drop its housing discrimination case instead of going to the Supreme Court. In exchange, the Justice Department reportedly declined to press False Claims Act charges against the city.

That has several GOP lawmakers, including Grassley, fuming.

Grassley said he probably wouldn’t try to filibuster Perez by himself but might join in with others if he doesn’t receive answers on the St. Paul case.

“That is what oversight is all about. … We have a responsibility to make sure the laws are faithfully executed. Getting our information is a big determination as to whether the law has been faithfully executed,” he said.

Ron Bonjean, a former GOP leadership aide, said the GOP can oppose Perez if it does it carefully and focuses “on his ability to promote jobs and the economy.” If Senate Republicans “start wading into the issues of immigration, that can be a political minefield for Republicans. Keep the focus on whether he can do the job,” Bonjean advised.

But Perez’s life story is sure to appeal to the groups the GOP now aims to court. One of five children of immigrants from the Dominican Republic, his four siblings became doctors while Perez became a lawyer. It’s a story right out of Obama’s stump speeches.