Mr. Clinton has promised to veto the GOP's $792 billion tax-cut plan and is expected to warn governors that the cuts will hurt state budgets.
Aides said Mr. Clinton also was expected to implore the governors to be more aggressive in enrolling children in the 1997 Children's Health Insurance Program in which Congress allocated the states $25 billion over five years to provide health coverage for children who do not qualify for Medicaid.
Mr. Clinton recently expressed disappointment that only about 1.3 million children have been enrolled in the new program, when he says should have at least 3 million covered by now.
Notwithstanding an element of prodding in his remarks, one aide said the president will assure the governors he is on their side and that he will resist any efforts in Congress to pull back unused welfare money or the unspent child health insurance funds.
The idea has already drawn criticism from some Republican governors who outnumber Democrats at the National Governors Association meeting 31-to-17. Governor Jesse Ventura of Minnesota is a member of the Reform Party. Governor Angus King of Maine is an independent.
Mr. Clinton flies to St. Louis Sunday from Little Rock, where Saturday night he headlined a fund-raiser for Vice President Gore.
Suspicious of their party leaders in Washington, Republican governors applauded Congress' tax cut plan Saturday but warned that they will not let GOP lawmakers raid state budgets to pay for it.
Republican congressional leaders have considered asking the nation's governors to return up to $6 billion in welfare money to help balance the books on their 10-year, $792 billion tax cut proposal.
Several governors accused fellow Republicans in Washington of trying to renege on pledges to ship the money to states. They suggested the development could damage their promised partnership with Washington.
"This must be a calamitous staff error, because I can't believe they would do this to us," said Gov. Frank Keating of Oklahoma, attending the four-day National Governors' Association meeting, which opened Saturday.
"They would lose a great deal of credibility and I don't think they want to do that," said Wisconsin Gov. Tommy Thompson, a national leader on welfare reform.
A growing force in Republican politics, the GOP governors said they are confident congressional leaders are preparing to back down.
But even the prospect of success has not dampened the state leaders' bitterness. For most governors, the first word of a plan to seek state money came from press accounts - not their leadership in Washington.
Governors do not like being kept out of the loop, especially after the leadership promised in 1998 to give them a greater role in framing policy and political strategy.