Supreme Court nominee Elena Kagan made her rounds on Capitol Hill, Wednesday, meeting with many of the lawmakers who will eventually have a hand in her confirmation.

Kagan's first stop was with Senate Majority Leader Harry Reid who said he'd make her confirmation process as "smooth as possible."

Republicans, however, told Kagan they want to make sure she'd be an impartial justice. The want to be sure her current post as the administration's Solicitor General would not influence her rulings based on the president's policies.

"This will be a challenging process to go through, it always is for a lifetime appointment of this consequence," Minority Leader Sen. Mitch McConnell said. "I want to assure her and assure the public that we intend to go through a thorough process."

Kagan's confirmation hearings are expected to start in late June or early July. President Barack Obama wants her in place in time for the start of the Supreme Court's fall term.