Senate Judiciary Republicans are performing a difficult balancing act as they intensify criticism of Supreme Court nominee Sonia Sotomayor in the run up to next month’s confirmation hearings.

From the outset, Republicans said they are interested in a fair, thorough and dignified confirmation process. But their minority role requires a rigorous probe of the speeches and judicial opinions of a nominee who could become the nation’s first Hispanic woman justice.

Texas Republican John Cornyn took exception when asked about GOP attacks on Sotomayor’s record on cases involving gun rights at a June 24 press conference.

“It is unfair to characterize what we are doing as an attack,” Cornyn said, adding, “We are committed to a fair and dignified process.”

Finding the right balance has proven most challenging for Alabama’s Jeff Sessions , the committee’s top Republican.

Sessions began the week of June 15 with a series of high-minded speeches focused on the proper role of judges. He quoted from the Federalist Papers and made little if any direct references to Sotomayor.

A week later, Sessions and other Republicans launched pointed critiques of Sotomayor’s views on gun rights and questioned her connections to a Latino legal advocacy group that Sessions said “has taken some very shocking positions with respect to terrorism.”

In another floor speech Thursday Sessions decried the influence of international law in American jurisprudence, saying Sotomayor, in a recent speech, “placed herself firmly on what I believe is the wrong side of this debate”

Democrats accused Republicans of a “fear and smear campaign” against the nominee. Ross Baker, a Rutgers University political science professor, said Republicans “are practicing the fine art of the non-denunciation denunciation.”

But Sessions—who was vilified and rejected by the Judiciary Committee as a failed federal district court nominee in 1986 — defended Thursday the GOP criticisms as compatible with a dignified process.

“We’re discussing matters of substance that directly relate to her role on the court, if she goes there,” the Alabama senator said. “Frankly, there’s some serious issues that have been raised that need discussion.”

He added, “I think it’s been dignified. The speeches have been at a high level. But this is not a judicial trial. We’re not required to not speak on the merits of it. This is a political process.”

But Republicans are caught between competing political imperatives. Barring some surprise revelation, GOP lawmakers are unlikely to derail Sotomayor’s nomination. A serious attempt to block her could harm the Republicans’ already dim political fortunes.