The senior Republican on the Senate Judiciary Committee even questioned whether Sotomayor sufficiently opposes terrorism, citing what he said was the "extensive work" she had done for a group formerly named the Puerto Rican Legal Defense and Education Fund.
"This is a group that has taken some very shocking positions with respect to terrorism," Sen. Jeff Sessions of Alabama said.
Sessions said the group, now called Latino Justice PRLDEF, in 1990 came to the defense of Puerto Rican nationalists who 36 years earlier had wounded five lawmakers during an attack on the House while it was in session.
Judiciary Committee Chairman Patrick Leahy of Vermont said PRLDEF is a mainstream group modeled on the NAACP Legal Defense and Educational Fund.
In multiple public and private speeches Tuesday, GOP senators began weaving a few select themes through their remarks and stepped carefully around others that could alienate constituencies Sotomayor represents. Without enough votes to filibuster or stop Sotomayor's confirmation to the Supreme Court, Republicans have few tools even to slow it down.
The Republican messaging from now through the confirmation hearings beginning July 13 includes issues popular among conservatives: Sotomayor's commitment to Second Amendment gun rights, her opinions on whether the Fifth Amendment protects against public takings without just compensation and on the equal protection clause of the 14th Amendment.
Sotomayor worked with the legal defense and education fund in 1990 when New York Mayor David Dinkins called the nationalist attackers "assassins," and a Puerto Rican Legal Defense and Education Fund official said Dinkins' terminology was insensitive.
"The president of the organization continued explaining, that for many people in Puerto Rico, these men were fighters for freedom and justice," Sessions said Tuesday. "So, I wonder if she agreed with that statement and if she agreed that the mayor of New York's comments were insensitive?"
Republicans said they have clarified their strategy in recent days by documents Sotomayor has turned over to the Judiciary Committee in advance of her confirmation hearings. But it was clear that with only seven Republicans on the 18-member panel and Hispanics and women already wary of the GOP, the party needs to tread carefully with any outright criticism of the first Latina nominated to the high court.
Democrats and Sotomayor supporters, meanwhile, scoffed at the notion that Republicans could stop or slow Sotomayor on substantive grounds, given her American dream background, Ivy League education and record as a federal judge.
"It has become clearer and clearer as we look at her record and vast experience that attacking this nominee is like throwing rocks at a library," said Sen. Bob Menendez, D-N.J. "It's uncalled for and it doesn't accomplish anything. Her opponents are grasping at straws."
"There's only one thing that can stop her and that is politics," said Art Acevedo, chief of police in Austin, Texas, and president of the National Latino Peace Officers Association, which endorsed Sotomayor on Tuesday.
But Republicans said they had substantive questions for Sotomayor.
Texas Sen. John Cornyn, a member of the Judiciary Committee and chairman of the GOP campaign committee, said he wants to know more about "whether Americans can count on her to uphold one of the fundamental liberties enshrined in the bill of rights: The right to keep and bear arms."
From the Second Amendment, Cornyn said he would move on to the Fifth - whether the government may take property from one person and give it to another, "based on some elastic definition of public use." Finally, Cornyn said he would move on to her thoughts on the equal protection clause in the 14th Amendment.
Republicans also want to know more about whether Sotomayor would hew to the Constitution and the law in her rulings or also employ the empathy that President Barack Obama said he wants in a justice on the high court. Sotomayor has told senators that a justice must ultimately and completely follow the law.
Sotomayor's comment that she hoped a "wise Latina" would come to better decisions than those who had lived other lives gets right at the empathy question. But Republicans are chastened by the public outrage that resulted when conservative commentators said that comment made Sotomayor a racist in reverse - then reversed themselves and backed off.
Instead, look for Republicans to say merely that the "wise Latina" concerns them - and then pivot to ask more broadly about her "judicial philosophy."
"As we consider this nomination, I'll continue to examine her record to see if personal or political views have influenced her judgment," Senate Republican leader Mitch McConnell said on the Senate floor.
That was all before lunch. Republicans then retired behind closed doors for their weekly policy session. There, Sen. Jon Kyl, the Republican whip, joined Sessions and Cornyn in a discussion of GOP strategy leading up to the hearings.
The leaders emerged describing the strategy as allowing her to explain "whether she's truly committed to colorblind justice."