Washington ? When Democratic voters are asked which politician they want as president, one name consistently appears at the top — Hillary Rodham Clinton. But the New York senator couldn’t make it any clearer that she isn’t running for the White House. At least not in 2004.

From her days as first lady, Clinton has accumulated political assets that are the envy of the announced Democratic presidential candidates: universal recognition, a nationwide network of supporters and an extraordinary ability to raise campaign cash.

She still is vilified by Republican fund-raisers but is getting bipartisan accolades for her conduct in the Senate. Her profile will be high in the coming weeks as she embarks on a media tour to promote her memoirs, “Living History,” which has a first-run printing of a million copies and goes on sale June 9.

Clinton insists she will not consider entering the race for president this year even if that is what some Democrats want. She has not ruled out a run in 2008.

“I just tell them that we have many other great candidates running for the job,” Clinton said, demonstrating a deference for her colleagues that has helped her win respect in the Senate.

Clinton took a low profile during her first two years as a senator. Now, she is taking a larger role.

“I think all of her colleagues on both sides respect her work ethic and the way she conducts herself,” said South Carolina Sen. Lindsey Graham. A conservative Republican, Graham worked with Clinton on legislation to extend benefits to military reservists.

Graham, a leader in President Clinton’s impeachment, said teaming with Sen. Clinton gave his reservist legislation the clout it needed to win Senate approval.

New York Sen. Hillary Clinton attends the Purple Heart First Day Stamp ceremony in Newburgh, N.Y. Clinton says she has no interest in running for the White House in 2004.

“People will attribute motives to her on anything she does,” Graham said. “I feel sympathetic to her situation as a junior member with such a high-profile status. It’s hard because people get jealous. She has handled this better than I think anyone expected.”

Clinton has gone out of her way to work with those on the opposite end of the political spectrum on policy issues such as the Middle East and foster care. Her partners have included House Majority Leader Tom DeLay of Texas, Sen. Arlen Specter, R-Pa., and even Sen. Elizabeth Dole of North Carolina, whose husband, former Sen. Bob Dole, lost to Bill Clinton in 1996.

Hillary Clinton also has taken on the GOP. She called the Republican leaders’ 2004 budget “the worst piece of fiscal legislation in the history of the republic” and described President Bush’s handling of the economy as the worst since Herbert Hoover.

Clinton, who does not face re-election until 2006, is among the Democrats’ leading fund-raisers. She spent $30 million to get elected and has raised about $3.4 million for her political action committee, HILLPAC, which she uses to support other Democrats running for office.

Her fund-raising and campaign skills could bring added interest in the senator as a potential running mate. She has said she would not accept the nomination for vice president, but Democratic sources close to Clinton say she might look at the ticket if the party’s nominee were well-positioned to oust Bush next year.