WASHINGTON -- Rep. Nancy Pelosi of San Francisco emerged Thursday as the early favorite to become the next House Democratic leader, but she faces a tough fight from a Texas challenger who says the party should move to the center, not to the left. 

Pelosi's contest with Rep. Martin Frost began in earnest after Rep. Richard A. Gephardt of Missouri announced he would step down as minority leader. Gephardt is mulling a bid for the presidency, and Democrats are pressing for new leadership after their disappointing performance in Tuesday's midterm elections. 

Pelosi last year became the first woman to hold a top congressional leadership job when Democrats elected her minority whip, their No. 2 post. If she succeeds Gephardt, she will make history again. She would not only become the highest-ranking female lawmaker ever in either the House or Senate, but she would also be the first Californian to lead a party in the House. 

She and Frost were working frantically behind the scenes to line up support for a secret ballot next Thursday by Democrats who will serve in the House's next session. In announcing their candidacies, Pelosi and Frost each promised to focus on the economy to help return their party to power. They also pledged sharper attacks on Republicans. 

"We must draw clear distinctions between our vision of the future and the extreme policies put forward by the Republicans," Pelosi said in a statement. "We cannot allow Republicans to pretend they share our values and then legislate against those values without consequence." 

Frost agreed. In a break with his party's preelection strategy of avoiding strong stands on tax policy, Frost said Democrats should consider whether to freeze those parts of President Bush's tax cut that benefit the wealthiest Americans. 

"You have to talk about fairness," Frost said in a news conference. "What's fair for the majority of American people?" 

Frost, who as caucus chairman ranks as the House's No. 3 Democratic leader, also attacked Pelosi. "Her politics are to the left," Frost said. "And I think that the party, to be successful, must speak to the broad center of the country." 

Debate among Democrats over how much they should concentrate on the center or the left of the political spectrum is a staple of contemporary politics; likewise, Republicans argue among themselves about whether to govern from the center or the right. 

But for the Democrats, defining their ideology has taken on new urgency after the party's losses Tuesday, which included at least five seats in the House. Many Democrats wonder whether they blundered in tactics, strategy or both. 

A number of factors favor Pelosi. She comes from the most-populous state. Besides Pelosi, California is sending 32 Democrats to the House's next session. Nearly all will vote for her. Frost has 16 Democratic peers in the Texas delegation. 

"We have the largest number of Democrats that any state has ever had," said Rep. Henry A. Waxman of Los Angeles, a Pelosi backer. "We know how to win elections. That's a job that's going to be important." 

Pelosi, 62, moved into the leadership more recently than Frost. She won her whip post in October 2001, defeating Rep. Steny H. Hoyer (D-Md.), 118 to 95. Much of the support she won then remains solid. Frost won his position four years ago. 

With close ties to Democratic donors from California, Pelosi also has raised millions of dollars for candidates around the U.S. 

Celebrity is another factor. As a woman in what is still a male-dominated Capitol, Pelosi draws an extra degree of attention. "What Democrats need is a charismatic leader that can help shape public opinion," said Rep. Janice D. Schakowsky of Illinois, a Pelosi backer. 

But Frost, 60, has plenty of credentials. He has served in the House for 24 years, longer than Pelosi's 15. He was chairman of the Democratic Congressional Campaign Committee for four years and knows the intricacies of redistricting. The senior Democrat on the House Rules Committee, he has influence over when and how legislation comes to the floor. 

His mostly liberal record is dotted with votes that give him ties to the party's moderate and conservative wings. Unlike Pelosi, he supported legislation to grant normal trade relations with China. In another break with Pelosi, he backed Bush on a recent resolution authorizing the use of force against Iraq. 

Backers say Frost is a more sure-footed political tactician. They point to an embarrassing episode during the recent campaign when several Democratic candidates were forced to return contributions they received from a Pelosi political action committee because of potential campaign law violations. 

Rep. John D. Dingell of Michigan, a leading Democrat, said he would support Frost as a leader who would "reach out to all parts of the party." He criticized Pelosi for showing a degree of "carelessness" with the campaign contribution gaffe. 

This year, Pelosi took the unusual step of supporting another Democrat, Rep. Lynn N. Rivers, against Dingell in a primary. Dingell won in a district that had been redrawn to pit the two incumbents against each other. 

Plenty of Democrats, loath to alienate either Frost or Pelosi, are likely to keep mum about their preference. One is Hoyer. 

"Both of them are good pols," he said. "They understand the public. Neither one of them is going to take us to the far left or far right." 

Gephardt, who has served as minority leader since 1995, was among the architects of a 2002 Democratic campaign strategy now being criticized for not offering a clear enough alternative to the Bush administration, especially on economic issues. 

He argued Thursday that factors outside his party's control -- the terrorist attacks of 2001 and an avalanche of special-interest money for Republicans -- left Democrats at a disadvantage. 

But Gephardt said Democrats should confront Republicans head-on about the economy, and especially about taxes, even if that means some political risk. "Better than tinkering around the edges is to come up with a complete alternative to the Bush tax policy," Gephardt said. "We need to have a roaring discussion." 

Gephardt declined to say whether he would support Pelosi or Frost as his successor.