Even as they continue to look for a smoking gun in the record of Supreme Court hopeful Sonia Sotomayor, leading Senate Republicans acknowledged on Tuesday that they have had a difficult time building widespread opposition to President Barack Obama’s first high-court pick.

GOP Senators now say their best bet for breaking into the public consciousness with their complaints about Sotomayor’s record may be during next week’s confirmation hearings — although privately, many said it may be too late to have any impact on the final vote.

“I think part of it is the Democrats are benefiting right now from the deluge of issues. They’ve got so many irons in the fire, it’s hard for anything to come through,— Senate Republican Policy Committee Chairman John Thune (S.D.) said Tuesday.

A senior Senate GOP aide who worked closely with the Bush administration during the 2005 and 2006 nominations of Chief Justice John Roberts and Justice Samuel Alito said Republicans haven’t been able to find one galvanizing issue around which to build opposition.

“We’re having the same problems that the Democrats had with Roberts and Alito,— the aide said. The Senate installed Roberts on a 78-22 vote in 2005 and Alito on a more partisan vote of 58-42.

Republicans have been trying to build a case that Sotomayor would take an activist approach to the bench. They also have taken issue with her affiliation with a Puerto Rican civil rights group and with some of her rulings on affirmative action and gun rights.

And while that case has resonated with the party’s conservative base, it has not piqued the interest of the general public — a problem that Thune and others said is due in part to the complexity of the issues and the length of her record.

“It takes a while to sort of download it all, process it all and digest it all,— Thune said.

Republicans said they are hopeful they can still use the hearings to build public opposition to Sotomayor’s installment on the high court. The hearings are set to kick off Monday.

“I do think when the hearings start next week is when people will start to pay attention to this nominee,— Thune said.

But the Republican aide warned that it is unlikely any major opposition will ultimately come about, noting that the GOP may have waited too long to mount an offensive.

“It’s the drawback to being reasonable. … If you know you’re going to oppose the nominee going in, it’s easy,— the aide said. The staffer pointed to Sen. Edward Kennedy’s (D-Mass.) speech at the beginning of the confirmation process for then-Supreme Court nominee Robert Bork as a classic example, noting that Kennedy essentially laid down Democrats’ marker and immediately began the process of building momentum against the 1987 nomination.

Despite the GOP’s setbacks with Sotomayor, however, the rhetorical war over her installment on the bench resumed Tuesday on Capitol Hill, with Senate Democrats touting her law-and-order credentials and Republicans and their allies searching for more weaknesses in her armor.

During a press event with the leaders of national law enforcement organizations, Judiciary Chairman Patrick Leahy (D-Vt.) once again hailed Sotomayor’s record on crime, using a new study by his staff to bolster claims that she is well within the mainstream of judges.

“It can be said with confidence that Judge Sotomayor is unquestionably a consensus judge on criminal issues. In fact, Judge Sotomayor’s criminal justice record proves that she is a moderate judge whose decisions in criminal cases rarely differ from those of her colleagues on the federal bench,— Leahy said.

But Senate Republicans argued that Sotomayor’s connections to a Puerto Rican civil rights organization suggest an activist approach to the judicial system.

Minority Leader Mitch McConnell (R-Ky.) in a floor speech argued that her work with the Puerto Rican Legal Defense and Education Fund and her controversial decision in an affirmative action case involving firefighters in New Haven, Conn., indicate a pattern of behavior.

“The perfunctory way in which she treated their case indicates either that she didn’t really care about their claims, or that she let her own experiences planning and overseeing these types of lawsuits with the Puerto Rican Legal Defense and Education Fund affect her judgment in this case,— McConnell said.

“Judge Sotomayor was in leadership positions with PRLDEF for over a decade. While there, she monitored the group’s lawsuits and was described as an ardent supporter’ of its litigation projects — one of the most important of which was a plan to sue cities based on their use of civil service exams. In fact, she has been credited with helping develop the group’s policy of challenging these types of standardized tests.—

At the same time, outside organizations continued to press the Senate on the nomination. The American Bar Association announced Tuesday a “well qualified— rating for Sotomayor — a judgment that Leahy called “further evidence of the outstanding experience she will bring to the Supreme Court.—

The National Rifle Association came out against the selection. In a letter to Leahy and Judiciary ranking member Jeff Sessions (R-Ala.), NRA Executive Director Chris Cox expressed the “National Rifle Association’s very serious concerns about the nomination of Judge Sonia Sotomayor,— particularly her involvement in a number of rulings on Second Amendment issues.