DENVER -- Senators from both political parties said they plan to question whether White House adviser Karl Rove may have given inappropriate assurances to conservative evangelical leader James Dobson in an effort to gain support for Supreme Court nominee Harriet Miers.

"When you know some of the things that I know, that I probably shouldn't know, you will understand why I have said ... that I believe Harriet Miers will be a good justice," Dobson said in his syndicated radio program.

Dobson is the founder of Focus On The Family, based in Colorado Springs, Colo.

Sen. Arlen Specter, R-Pa., chairman of the Senate Judiciary Committee, said his committee "is entitled to know whatever the White House knew" regarding Miers and her views on important legal issues.

"If there are back-room assurances, and if there are back-room deals, and if there is something which bears upon a precondition as to how a nominee is going to vote, I think that's a matter that ought to be known by the Judiciary Committee and the American people," Specter said Sunday on ABC's "This Week."

Sen. Patrick Leahy of Vermont, the ranking Democrat on the committee, said he would oppose any nominee who gives assurances about how he or she would vote on particular cases.

"I would vote against that person," he said. "I wouldn't care whether they are nominated by a Democrat or a Republican ... and all 100 senators should vote against them under that basis alone."

Leahy said Miers has told him that she has given no such assurances.

The White House acknowledged Rove has been among those making calls to key conservative supporters but denied anything improper has been promised.

Dobson said last week that he had spoken in confidence with Rove about the Miers nomination and that their conversation convinced him to support her. He wouldn't say what he was told about her political beliefs, or what led to his support of Miers.

Both Leahy and Specter said they might call Dobson and Rove to clear up the matter. However, it is doubtful that Rove would agree to testify before the committee, since as a presidential adviser he is subject to a White House declaration of executive privilege.

A spokesman for Focus on the Family said Sunday it was premature to discuss a possible appearance by Dobson on Capitol Hill.

"Dr. Dobson has received no such invitation from the Senate and will wait until it comes to respond," the spokesman said.