MIAMI -- A number of Democratic state chairmen -- who generally represent the center of their party -- have bluntly warned President Bush that public support for his Persian Gulf policies is waning fast.

During meetings here Friday and Saturday, the chairmen said in interviews that Bush will face a significant challenge on the domestic front if hundreds of thousands of U.S. troops remain in Saudi Arabia after Christmas without better justification.

"It's at the teetering point -- the people are really becoming skeptical," Pennsylvania Democratic Chairman Larry Yatch said about public support for Bush's Iraq-Kuwait policies. "Voters are coming to the stark realization that this isn't going to be a Grenada. They are realizing that there could be serious loss of lives and casualties."

While intensely partisan, Yatch and most of the Democratic chairmen meeting here tend to make their political assessments based on what they believe are the opinions of swing voters whose ballots they must win to carry general elections. All of the chairmen arrived here just after completing a year or more of intensive campaigning in their home states.

James J. Brady, Louisiana chairman and a solid southern moderate, said voters in his state generally are supportive of the U.S. military but Bush "has not given them answers to their questions." Assertions that the military intervention is a "jobs" program does not sell in Louisiana, Brady said. "Jobs are not the reason we are there," he said.

Asked how much longer Bush can depend on majority support, Brady said: "Not long, maybe a month to six weeks. . . . Bush has just got to come up with strong reasons for being there." A number of his counterparts from other states echoed those sentiments.

Among those interviewed here at the meeting to start preparations for the 1992 election, there was a consensus that a key turning point is likely to be the Christmas-season holidays, if nothing major happens before then.

Florida Chairman Simon Ferro said that not only will television viewers across the country see U.S. troops far from home during the holiday period, but their relatives -- "their mothers, fathers, wives and husbands" -- will begin to really feel the pain "of missing loved ones. The timing over the next weeks is not great."

Along similar lines, Ohio Chairman James Ruvolo initially said he thought Bush had about another six months before public hostility to the military venture became politically dangerous. But upon thinking about the approaching holidays, he said, "it could well be quicker. Bush still has time, but it is going to wear out." The public, he said, does not see a great moral purpose in U.S. invovement in the gulf. "Most people think this is about oil, not about anything else," he said.

It is the lack of publicly accepted justification beyond protecting oil interests that will make it difficult to sustain support for a policy requiring U.S. military personnel to spend Christmas in a desert with the constant threat of chemical warfare, Ferro, Ruvolo and others argued.

Texas Democratic Chairman Robert Slagle said he did not fully realize the depth of the issue until the men and women overseeing campaign phone banks began reporting to him that voters, without prompting, were beginning to ask worried questions about the gulf operation. This was particularly true of Mexican American women, many of whom have children serving in the military in the Middle East, Slagle said.

The least worried of the chairmen interviewed about the gulf during the meeting of the Association of State Democratic Chairs was Ray Powell, chairman of the New Mexico Democratic Party. "Most {New Mexico} voters generally support the president on this, they support him to this point," he said, but added, "It's gradually changing."