WASHINGTON (CNN) -- The White House on Monday began a renewed attempt to rally backing for Harriet Miers, the Texas lawyer whose nomination to replace retiring Justice Sandra Day O'Connor on the U.S. Supreme Court has failed to attract widespread support from any part of the political spectrum.Flanked by six current and former justices of the Texas Supreme Court who vouched for the qualifications of the former president of the Texas Bar Association, President Bush said, "They are here to send a message here in Washington that the person I picked to take Sandra Day O'Connor's place is not only a person of high character and integrity but a person who can get the job done. Harriet Miers is a uniquely qualified person to serve on the bench."Bush has described Miers as "a pioneer of law" in Texas, where she was the first woman to become a partner in her Dallas law firm and the first female president of the Dallas and Texas bar associations.She has worked for Bush since 1994, most recently as White House counsel.'Pivot day' on nomination"Mr. President, we just all want to thank you for this nomination," said John Hill Jr., a Democrat who was chief justice of the Texas Supreme Court from 1985 to 1988 and served with Miers on the Texas Lottery Commission."We are excited about it, and we are here to try and let the people of America know what we all know, which is that she is an absolutely fantastic person and a great lawyer and will make a great judge," he said.Asked about the event, White House press secretary Scott McClellan said the men are qualified to attest to the abilities of the nominee."These are former justices of the highest court in Texas who know Harriet Miers very well," he told reporters. As someone who has not "sought the limelight," Miers is only now becoming known to the American people, he said. "We want the American people to get to know Harriet Miers like the president knows her," McCellan said.A Bush official said over the weekend that Monday would be "pivot day" on the administration's strategy to drum up support for Miers, whose membership in an evangelical, conservative church failed to ignite support among anti-abortion activists, the GOP establishment or key Democrats."We actually know Harriet Miers; I hope that still counts for something, somewhere," Hill said. "I'd trust her with my wife and my life."Miers has never served as a judge, but Hill said that is not a critical drawback. "You get the briefs, you hear the arguments, you study the facts, you study the law and you try to make a square decision based on the law and the Constitution, and I don't think it matters that much whether you were a judge before," he said.Miers was on Capitol Hill on Monday. By the end of the day, she was to have visited 18 senators -- including Senate Judicial Committee members Sens. Charles Schumer, D-New York, and Dianne Feinstein, D-California -- in her quest for approval, McClellan said.Conservatives dividedBush's decision to name Miers, his White House counsel and a longtime adviser, to the Supreme Court has divided even his supporters, many of whom had hoped for a nominee with a clear record of opposition to abortion. Miers has left few clues to her position on that issue in her previous public posts, which include service on the Dallas City Council and as Bush's lottery commissioner when he was governor of Texas.Miers' nomination also has failed to attract much popular support. In a CNN/USA Today/Gallup Poll released Monday, 36 percent of respondents said Bush should withdraw her nomination, versus 46 percent who opposed the idea and 18 percent who said they were unsure. The question on withdrawal had a sampling error of plus or minus 5 percentage points.The poll of 1,012 American adults was carried out Thursday through Sunday.Forty-four percent of respondents said they felt the Senate should confirm her, 36 percent expressed opposition and 20 percent said they were unsure. That question also had a sampling error of plus or minus 5 percentage points. Asked their opinion of Miers, 31 percent described it as favorable, 26 percent as unfavorable and 43 percent said they were unsure. That portion had a sampling error of plus or minus 3 percentage points.In an editorial last week, the conservative weekly magazine National Review called on Miers to withdraw."Leaving aside the president and his employees, even Miers' fiercest defenders allow that she was not their top pick -- or even their 10th," the editors said."As one of her former colleagues has said of her, Miers' office was the 'place where the action stopped and the hand-wringing began.' If she follows that course, we will be left with a court that retains immense and inappropriate lawmaking power but refuses to make clear laws."