WASHINGTON—Supreme Court nominee Sonia Sotomayor determinedly sidestepped volleys of Republican questions on abortion and gun rights Wednesday, keeping her demeanor cool and her opinions mostly private as she neared the end of a marathon Senate grilling on the road to all but sure confirmation.

After two long days of questioning by Judiciary Committee senators, Sotomayor had yet to make a slip—certainly not the gaffe that even Republicans concede would be necessary to derail her nomination to be the first Hispanic and third woman to serve on the high court. She was due back for still more questioning on Thursday.

The appeals court judge, 55, avoided weighing in on any major issue that could come before her as a justice, instead using legal doctrine, carefully worded deflections and even humor to ward off efforts to pin her down.

Appearing more at ease in the witness chair, Sotomayor defused a tense exchange on gun rights by joking about shooting a GOP critic and charmed Democratic supporters with nostalgic praise for fictional attorney Perry Mason.

Republicans, frustrated in their attempts to undercut President Barack Obama’s first high court choice, said they were still worried Sotomayor would bring bias and a political agenda to the bench.

“It’s muddled, confusing, backtracking on issue after issue,” complained Sen. Jeff Sessions of Alabama, the top Republican on the Judiciary panel. “I frankly am a bit disappointed in the lack of clarity and consistency in her answers.”

Her rulings—except for a much-debated reverse discrimination case—have not shed much light on her positions either, though she is considered unlikely to disturb the Supreme Court balance in replacing generally liberal Justice David Souter.

On abortion rights for example, Sotomayor has not ruled on any case that squarely confronts the issue. As an appeals court judge she dismissed a challenge to the so-called global gag rule on U.S. foreign aid, deciding against an abortion rights group. But in her opinion she used the phrases “anti-abortion” and “pro-choice,” typically used by abortion rights supporters.

The hearings are expected to continue Thursday with more questions for Sotomayor and testimony from outside witnesses. A vote by the full Senate to confirm her is expected in early August, time enough to allow her to don the robes of a justice before a scheduled hearing on Sept. 9 on a case involving federal campaign finance law.

The cavernous hearing room on Capitol Hill was filled for a third straight day, and tourists waited in line outside for their few moments to witness history.

Among the audience members sat Frank Ricci, a white New Haven, Conn., firefighter whose reverse discrimination claim was rejected by Sotomayor’s court panel. The Supreme Court overturned that ruling late last month, and Republicans plan to showcase Ricci on Thursday as part of their effort to portray her as a judge who has let her biases trump the law.