WASHINGTON — A week before Supreme Court nominee Sonia Sotomayor's Senate hearings, Republicans are floundering in their efforts to trip her up, unable to find an effective message about why she's not fit to serve.

Blame the tricky politics of opposing the woman who would be the first Hispanic justice, especially for a party struggling to broaden its base.

Add to that the mathematical impossibility of Republicans' rejecting President Barack Obama's first high court nominee, and it's a recipe for a weak-kneed response.

Conservative activists have noticed, and they're not happy.

"Too many Republicans and conservatives planned to lose instead of planning to win" the debate over Sotomayor, said Tom Fitton of Judicial Watch. His group has mounted strong opposition to the federal appeals court judge.

About half the Senate's Republicans are willing to raise serious questions about Sotomayor and there's "a sizable minority who — partly because she's Hispanic — just want this to go away," said Curt Levey of the Committee for Justice.

Conservative groups have sought to convince Senate Republicans that they can benefit politically by strongly opposing Sotomayor. But many of their leaders complain the message isn't getting through.

During recent confrontations, some activists have told GOP senators, "Don't throw away yet another conservative agenda item when it's a successful one for you. Your base cares about this and you should, too," said former Rep. David McIntosh, R-Ind., who's advising some outside groups on Sotomayor's nomination. "It was kind of a blunt message."

There are good reasons for Republicans to be holding back, wondering what their best approach is to opposing a nominee who's broadly acknowledged to be qualified and whose past rulings make it difficult to pigeonhole her as a liberal crusader.

The GOP has just 40 votes in the Senate — well short of the majority they would need to defeat Sotomayor or to sustain a drawn-out effort to block a final vote to confirm her.

Even if they could stall Sotomayor's nomination, though, it's evident that many Republicans don't think it's politically prudent to take on a Hispanic woman, given the GOP's low standing in the polls and its efforts to appeal to women and minorities. Those groups traditionally have shunned the party.

For instance, Republicans recently banded together to raise concerns about her position on gun rights. They held a news conference about an appeals court decision Sotomayor joined that said the Second Amendment's protection against curbs on bearing arms applies only to the federal government — not to states.

That was in line with Supreme Court precedent on the issue, Alabama Sen. Jeff Sessions, the senior GOP member of the Senate Judiciary Committee, acknowledged, and presumably in keeping with GOP views that judges should be restrained.

But Sen. John Cornyn, R-Texas, criticized Sotomayor for taking a "cramped and restricted view of a basic civil liberty." At the same time, Sen. Orrin Hatch, R-Utah, said Sotomayor had been too expansive in her ruling on the right to keep and bear arms. "I wish Judge Sotomayor had been similarly restrained on these issues" as other courts that ruled differently, he said.

The GOP message was as clear as mud.