As Supreme Court nominee Elena Kagan plans to visit Capitol Hill and meet with senators Wednesday, one Republican lawmaker reiterated that he will oppose her nomination, just as he did 15 months ago when she was nominated for her current post as solicitor general.

Sen. James Inhofe, R-Oklahoma, estimated more than half of the Senate has already made up their minds on Kagan - even if they haven't said so publicly.

"They just don't say it," he said. "I say it."

"We went through the confirmation process 15 months ago and nothing has changed since that time,"  he said

Inhofe told CNN the main sticking point for him was Kagan's decision, while dean of Harvard Law School, to block military recruiters from the law school's campus in protest of the Pentagon's policies preventing gays and lesbians from serving openly in the military.

Other Republicans have also expressed concern about the issue. They include Jeff Sessions of Alabama, who is scheduled to meet with Kagan Wednesday. Sessions, the top Republican on the Senate Judiciary Committee, has said Kagan "made a big mistake ... Was that disqualifying? I don't know. We'll see. But it's a significant issue."

Inhofe also pointed to Kagan's lack of judicial background, noting it has been 38 years since a justice with no experience on the bench has been confirmed. However, he said that issue was not a "deal killer" for him, although he said that a nominee with prior judicial experience is preferable.

Asked whether Kagan's stance on campus military recruitment was rooted in opposition to the "Don't Ask Don't Tell" policy, and not an indictment on campus recruitment per se, Inhofe said he fails to see a connection. "My concern was, if you're recruiting, you ought to be able to recruit on campuses."

He accused Kagan of flip-flopping on "Don't Ask Don't Tell," pointing out she was an aide to former President Bill Clinton and at one time supported the policy. "She's changed her mind since then, apparently," he said.

Clinton picked her in 1999 for the powerful U.S. Court of Appeals for the D.C. Circuit. But no Senate confirmation hearings were held, and the nomination lapsed. The seat was later filled by John Roberts, who quickly used the appointment as a springboard to chief justice of the Supreme Court.

Inhofe said if he opposes someone's nomination, he does not change his mind when that person is nominated for a higher position later. "If I believe someone is not qualified for a lower position, like a district level, how could that person be qualified for the United States Supreme Court? I don't think they could. The bar has to go up as you go up the courts."

Asked if there is anything Kagan could say to change his mind, he said that although he is not a member of the committee, "I would watch very carefully - I would say no."

Kagan also plans to meet Wednesday with Senate Majority Leader Harry Reid, D-Nevada; Minority Leader Mitch McConnell, R-Kentucky; Patrick Leahy, D-Vermont; and Dick Durbin, D-Illinois, White House spokesman Robert Gibbs has said.

President Barack Obama nominated Kagan Monday to replace retiring Supreme Court Justice John Paul Stevens. If confirmed, Kagan, 50, would become the 112th Supreme Court justice, the third woman on the current nine-member bench and the fourth woman in the court's history.