Solicitor General Elena Kagan wrapped up her testimony before the Senate Judiciary Committee on Wednesday night with no major faux pas, having provided Republicans no ammunition likely to prevent her from becoming the fourth woman to serve on the Supreme Court.

Although the committee will meet Thursday to hear from outside witnesses, Kagan’s time before the panel is done. Chairman Patrick Leahy (D-Vt.) called the end of her testimony “the last time you will have to be in a public airing before the Senate Judiciary Committee.”

With Republicans on the committee doing little in the end to slow the momentum of Kagan’s nomination, Republicans off the committee privately questioned ranking member Jeff Sessions’ (Ala.) stewardship of the opposition.

One Republican operative — who asked not to be identified in order to frankly discuss Sessions’ efforts — acknowledged that many conservatives are unhappy, believing the committee did not focus enough on a handful of potentially incendiary issues such as Kagan’s involvement in the 1990s partial-birth abortion debate, hitting her instead on less-explosive topics such as her views on the military.

“There is a fair amount of frustration in conservative circles that there were huge liabilities left virtually untouched by Republican Senators in these hearings. If a Republican nominee would’ve had a fraction of the issues Elena Kagan has in her record as a political operative and policy adviser we’d be looking for a new nominee,” the Republican said Wednesday.

But a Senate Republican aide dismissed criticisms of the Judiciary Republicans’ showing, arguing that Kagan’s efforts to avoid answering difficult questions “did not stop Republicans from artfully and intently engaging the nominee on a wide range of core issues.”

“Kagan’s answers to a number of questions have expanded existing concerns, including her comments on the extent of government power and her mistreatment of the military in defiance of the law. Judiciary Republicans put on an impressive display throughout the week,” the aide added.

Republican Senate aides also lamented the timing of outside events that have eclipsed the hearing. The death Monday morning of Sen. Robert Byrd (D-W.Va.) not only cast a pall over the proceedings but also led Leahy and Sessions to agree to limit the hearings to three and a half days, rather than the expected four or five, to accommodate Byrd’s memorials.

And Tuesday, the Armed Services Committee held hearings on the confirmation of Gen. David Petraeus to become the top general in Afghanistan.

With Kagan making no news, the hearings flew largely beneath public notice. By Wednesday, many cable news networks were no longer carrying the proceedings full time, instead devoting significant time to the Petraeus and Byrd stories — and in some cases the retirement of legendary television personality Larry King.

Republicans did score some hits Wednesday, most notably during questioning by Sens. Orrin Hatch (Utah) and Lindsey Graham (S.C.) on the partial-birth-abortion issue.

Hatch, in particular, took Kagan to task for her role in an alleged effort by the Clinton White House to force the American College of Obstetricians and Gynecologists to modify a position paper on partial-birth abortion. An original draft of the paper opposing the practice did not include language endorsing an exception for cases in which a mother’s life is at risk.

But the final paper did include that language, and Republicans argued Clinton-era memos showed Kagan had been instrumental in getting the paper changed.

Although Kagan acknowledged that “we did have some discussions about clarifying” the position paper with ACOG, she maintained the White House did not pressure the organization to change it.

“There was no way in which I would have or could have intervened with ACOG, which is a respected body of physicians, to get it to change its medical views on the question,” Kagan said.

Hatch’s concerns remained. “I just want you to know I’m troubled by it. And even though I care a great deal for you and respect you,” he said.

But by midmorning Wednesday, even Republicans appeared to be throwing in the towel, acknowledging that Kagan would likely be confirmed.

“I assume she will be,” Sen. John Cornyn (R-Texas) said Wednesday morning. Minority Whip Jon Kyl (R-Ariz.) added, “With only 41 votes, I think a filibuster would be highly improbable.”

Cornyn, meanwhile, found himself in the awkward position of having to use part of his second round of questions Wednesday afternoon to perform damage control.

Cornyn and several other Republicans on the committee have come under attack from liberals for their criticisms of former Justice Thurgood Marshall.

Marshall was one of the chief architects of the civil rights movement and has long been criticized by conservatives for what they call his activist interpretation of the Constitution. Liberal commentators have accused Marshall’s critics of racism.

Noting a Wednesday morning opinion piece attacking him for criticizing Marshall, Cornyn asked Kagan if she felt he had been disparaging Marshall, for whom Kagan had clerked in the 1980s.

“There were some folks — or actually an op-ed that was published today — that suggested that those of us who talked about Justice Marshall and — and talking about his judicial philosophy — were somehow disparaging Justice Marshall,” Cornyn said.

“Did you read any disrespect in any of the comments that any of us have made about Justice Marshall?” he added.

Kagan, appearing to be caught off guard, dismissed attacks on Cornyn and agreed he was acting “in good faith.”

“I take everything that has been said here from all the way around the bench as people operating in good faith and certainly I’ve … gotten nothing but fairness and courteousness from everybody, from every member of the committee, and I take no offense on behalf of myself or on behalf of Justice Marshall or on behalf of anybody else,” she said.