(CBS/AP) With Harriet Miers still under attack from the right, President Bush is launching a new, more aggressive strategy in defense of his Supreme Court nominee.

The White House wasn't expecting conservative opposition and it spent much of last week on the defensive. This week, the president and members of the administration are trying to frame the debate around Miers' legal qualifications, reports CBS News senior White House correspondent Bill Plante.

Secretary of State Condoleezza Rice was among those vouching for Miers on Sunday.

"She is a woman with extraordinary integrity and talent. She is the kind of person that if there have been four arguments given she's going to look for the fifth. She's got a very probing mind and a very probing intellect," Rice told Fox News.

Mr. Bush will be joined in the Oval Office on Monday by two former justices from the Texas Supreme Court, one of them a Democrat, who will help him make the case that Miers has the legal skills needed to serve on the U.S. Supreme Court.

CBS News correspondent Susan Roberts reports the administration is primarily fending off critics inside the Republican Party who say the Texas native with a career as a lawyer and legal adviser is a risky pick because she lacks the experience of a proven conservative judge.

Trying to calm conservative furor last week, the White House stirred up more controversy by highlighting Miers' religious beliefs.

"Part of Harriet Miers' life is her religion," President Bush said last Wednesday.

Some Democrats said the president's comments did not help his nominee.

"What the president has done is set up a standard for Miss Miers which is going to make it very difficult for her at the hearing," said Sen. Richard Durbin, D-Ill., a member of the Senate Judiciary Committee.

Miers returns to Capitol Hill Monday, meeting with more members of the Judiciary Committee who are trying to pin down her judicial philosophy and likely positions on the contentious issues slated to come before the high court.

Miers is scheduled to meet with Democratic Sens. Dianne Feinstein of California and Charles Schumer of New York. Both voted against confirming John Roberts as chief justice.

On Sunday, Feinstein criticized what she called attacks on Miers from the Republican right and said she is interested in learning about Miers' judicial philosophy.

Feinstein told CNN her questioning during the hearings will focus on whether Miers can rule independently and show a "breadth of knowledge" on various issues.

Other Democratic committee members also said they want to know more about Miers' views on issues likely to come before the court.

"We all have a right to know where she stands on these basic issues," Sen. Joe Biden, D-Del., told CBS' Face the Nation. "And I hope this puts to bed this notion that it's not a legitimate thing for the United States Congress to find out where a nominee stands on the fundamental constitutional questions facing her."

Meanwhile, a leading Republican, Sen. Chuck Hagel of Nebraska, dismissed as "nonsense" suggestions that sexism and elitism were behind the opposition to Miers.

"The fact is this is an elite group of individuals. The fact is we want an elite group of individuals," Hagel told CBS.

"I'm not so sure I want my next-door neighbor, as much as I like him or her, to be on the Supreme Court because they're nice people."