"I think this is an excellent choice by the president of the United States and I think when people get to know her and understand her like we do they'll find her an excellent choice. And she'll be a legend on that court before her career is finished," said one of the Texans, Craig Enoch.
The photo op with the former jurists was part of a new effort by the White House to counter criticism that Miers lacks the qualifications for the high court.
"Harriet Miers is a uniquely qualified person to serve on the bench. She is smart, she is capable, she is a pioneer," Mr. Bush said after meeting with the Texas judges. "She's been consistently ranked as one of the top 50 women lawyers in the United States. She has been a leader in the legal profession. She's impressed these folks. They know her well. They know that she'll bring excellence to the bench."
Meanwhile, Miers arranged personal meetings during the day with Democratic Sens. Chuck Schumer of New York and Dianne Feinstein of California. Both are members of the Judiciary Committee, which will hold hearings and take the first vote on the nomination.
Senate Republicans hope to begin confirmation hearings on Miers the week of November 7, officials said Monday.
Officials in both parties said Republicans have proposed a schedule for Miers' confirmation process that calls for a vote in the full Senate before Thanksgiving. It was not clear whether Democrats would agree or seek changes.
The two parties haggled at length earlier this year over a confirmation timetable for John Roberts, eventually confirmed as chief justice.
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.
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."