AUSTIN — Houston Mayor Bill White said Monday that he is considering running for governor after Fort Worth attorney Tom Schieffer ended his candidacy and urged his former rivals to embrace White as the Democratic Party's consensus candidate.

The remaining Democratic contenders in the 2010 governor’s race, however, all rebuffed Schieffer's suggestion and vowed to press ahead with their campaigns.

White, who is running for the U.S. Senate, announced that he is considering switching races to enter the Democratic gubernatorial primary. He said he will decide Dec. 4 after hearing from the public.

The rapid-fire developments, which come in advance of the Dec. 3 start of the month-long candidate filing period, would abruptly alter both the governor’s race and the Senate race.

Schieffer, a U.S. ambassador in the Bush administration, was the first major candidate to enter the Democratic primary race for governor but struggled to ignite enthusiasm and raise money.

"I just couldn't convince enough people that I could win," he said in announcing his withdrawal from the race at a state Capitol news conference.

Schieffer told reporters that he met with White on Sunday and urged him to run.

White, he said, offers the experience, fundraising skills and conservative-to-moderate credentials need to beat the winner of the Republican primary race between Gov. Rick Perry and his challenger, U.S. Sen. Kay Bailey Hutchison.

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