Senate Republican leaders are launching a full-on assault against President Barack Obama’s Supreme Court nominee, Elena Kagan, over her lack of judicial experience, but they already appear to have a major problem: Their rank-and-file Members aren’t buying into it.

Soon after Obama announced Monday the solicitor general as his nominee to replace retiring Justice John Paul Stevens, GOP leaders took to the Senate floor to raise doubts about her ability to serve, arguing that she has never been a judge and had little courtroom experience.

National Republican Senatorial Committee Chairman John Cornyn (Texas) called Kagan “a surprising choice” and said: “Most Americans believe that prior judicial experience is a necessary credential for a Supreme Court justice.”

Senate Minority Leader Mitch McConnell further highlighted how Kagan, a former professor and dean of the Harvard Law School, not only lacks judicial experience, but substantial litigation experience as well.

“Ms. Kagan has neither” of these qualifications, the Kentucky Republican said, which sets her apart from former Chief Justice William Rehnquist, who also lacked judicial experience but was in private practice for 16 years prior to his appointment to the court.

“We will diligently review Ms. Kagan’s record to ensure … that she possesses the requisite experience to serve on the Supreme Court,” McConnell vowed.

But the aggressive posture doesn’t appear to be resonating with many of the rank and file, who say that her lack of judicial experience should not be used against her.

Judiciary Committee member Sen. Orrin Hatch, who said he knows Kagan personally, said she is “fair” and has “a good résumé.” He dismissed concerns about her time in the courtroom.

[IMGCAP(1)]”I do not think it’s a disqualifier not to be a sitting judge. Some of the greatest judges on the court were not sitting judges,” the Utah Republican said. “I suspect she’ll do fine” in the confirmation hearings.

Similarly, Sen. John McCain said he doesn’t have a problem with the amount of time Kagan has spent on the bench. “That wouldn’t be my concern,” the Arizona Republican said.

Moderate GOP Sen. Olympia Snowe (Maine), who was one of seven Republicans who voted last year to confirm Kagan as solicitor general, said she didn’t think it was necessary that all Supreme Court justices have a judicial background.

“I think you have to look at the totality of one’s experiences,” Snowe said. “We have to make sure that there is a broad perspective.”

The inconsistency in GOP messaging also seemed to come through in Cornyn’s own critique of Obama’s selection. Asked earlier this month about the possibility of Obama nominating a woman, Cornyn said there are “a number of highly qualified [women], including Elena Kagan and Diane Wood.” After Monday’s announcement, however, Cornyn blasted Kagan for having spent her “entire professional career in Harvard Square, Hyde Park and the D.C. Beltway,” which he said are “not places where one learns ‘how ordinary people live.'”

A Cornyn spokesman said Tuesday that there was no contradiction in the Senator’s words since his earlier comments were about there being a wealth of female lawyers in the country.

Both Kagan and Wood are “first-rate intellects. There are a lot of pedigreed lawyers, but that doesn’t mean they should all be on the Supreme Court,” the spokesman said.

At least one Republican leadership aide downplayed divisions within the Conference, saying that a united front on the Supreme Court nomination process is nearly impossible and that charges over Kagan’s experience are simply a prelude to a larger critique of her record and philosophy.

“The lack of experience isn’t the put-away shot,” the aide said. “It’s the door we use to get into her record.”

Another GOP aide agreed and said that Republicans are planning to attack not only her résumé but also her ability to shift from being the Obama administration’s top lawyer to an impartial judge.

“If confirmed, she must prove that she wasn’t selected to continue on in that role” as solicitor general, the aide said.

The White House has already begun its campaign to pick off support from moderate Republicans. On Monday, just hours after Kagan’s nomination became official, Chief of Staff Rahm Emanuel called Snowe and Sen. Susan Collins (Maine) to discuss the nomination process. And President Barack Obama called recently elected Sen. Scott Brown, who said Obama didn’t ask him to vote for Kagan but to keep an open mind.

“I said, ‘You know me by now, of course I am,'” the Massachusetts Republican said Tuesday.

Obama is also taking steps to make sure his own party is on board with Kagan’s nomination. The president on Tuesday dispatched White House counsel Bob Bauer, who has been Obama’s point person in the Supreme Court confirmation process, and Phil Schiliro, assistant to the president for legislative affairs, to the Hill to talk to Senate Democrats during their weekly lunches.

Sen. Dianne Feinstein (D-Calif.), who sits on the Judiciary Committee, said afterward that Bauer and Schiliro told Democrats that they just “wanted to help” and if there was “anything that we needed, let them know and they’d get it to us right away.”

Sen. Barbara Mikulski (D-Md.) said the White House officials also indicated that they are “organizing a war room” to help push Kagan through the Senate. Obama wants Kagan confirmed before Labor Day, and senior Senate Democrats have suggested that a summertime confirmation vote is likely.

Kagan is scheduled to begin making the rounds in the Senate on Wednesday. She has meetings lined up with Majority Leader Harry Reid (D-Nev.), McConnell, Majority Whip Dick Durbin (D-Ill.), Judiciary Chairman Patrick Leahy (D-Vt.) and ranking member Jeff Sessions (R-Ala.).