President Clinton renewed his threat to veto a Republican-passed tax cut bill, but told the nation's governors he remains hopeful that the administration and Congress can reach a compromise and avoid a budgetary train wreck this fall.

Speaking to the National Governors' Association meeting, Clinton also appealed to the governors to redouble their efforts to provide health insurance for children. But many of the state executives challenged the administration's contention that they have moved slowly to implement a new federal health care plan. Many said where they have been slow, Washington is to blame.

Clinton and Senate Majority Whip Don Nickles (R-Okla.) also reassured the governors that they would resist any efforts by members of Congress to take back unused welfare funds that have been building up in the states since the approval of a reform plan three years ago.

Clinton and Nickles, in back-to-back appearances, outlined the arguments for and against the $792 billion tax cut bill approved by the Republican-controlled Congress last week--a debate that is expected to rage through the August congressional recess as both sides position themselves for expected negotiations in the fall.

Clinton said Congress could not cut taxes by nearly $800 billion and provide additional funding for economically beleaguered farmers, national defense and other areas without having to dip into projected Social Security surpluses.

He also warned that a big tax cut would trigger an interest rate hike by the Federal Reserve. "People will lose what they get in a tax cut in higher interest rates," he said.

Clinton, stressing deep differences with the GOP, nonetheless told the governors, "I am not nearly as pessimistic as a lot of people are about the prospects of our reaching an agreement, and I am determined to do so."

Nickles also signaled willingness to compromise, but rejected claims that the Republican bill threatens the economy or the financial soundness of Social Security. With projected surpluses of $3 trillion over the next 10 years, he said it was time to let taxpayers keep "their money."

Leaders from both parties used the Sunday talk shows to carry on their tax debate. White House Chief of Staff John Podesta said on NBC's "Meet the Press" that the GOP bill was "a bad deal" for the American people that would "cause deep cuts in important programs."

Senate Majority Leader Trent Lott (R-Miss.), interviewed on ABC's "This Week," called Podesta's remarks "at the minimum a misstatement or downright lies."

Administration officials said the bill would necessitate cutting Medicare by $31.8 billion, farm safety net programs by $18.9 billion, veterans' benefits by $3.1 billion and child support enforcement by $10.2 billion. But all the number-crunching amounts to little more than political posturing given that Clinton has vowed to veto the tax package.

If the two sides reach a stalemate over the last few major spending bills, the government could be faced with a repeat of the 1995 government shutdown, for which the Republicans were blamed. Lott said today, "I don't know of anybody who is looking for the so-called train wreck. There's no need for that sort of thing. And it's irresponsible, too."

Despite the partisan lines that have been drawn in Washington, many governors predicted an eventual compromise. "I think governors at one level understand that they've got to come together on this," said Michigan Gov. John Engler (R). "We've got to have a budget."

But Engler said he believes many Republican governors see no reason to have a big fight over taxes this close to the 2000 elections. "Why spill a lot of blood over this right now?" he said. "Let's work toward being able to write the perfect plan in 2001."

The governors were more animated in their response to Clinton's comments about the Children's Health Insurance Program (CHIP). Clinton said that while many states have made progress enrolling children in the new program--which is aimed at low-income families that do not qualify for Medicaid coverage--much more should be done.

"I think there is an enormous amount of progress that is still to be fulfilled here," he said.

Clinton said the federal government would write to school superintendents and school principals urging them to increase efforts to identify eligible children. He also said the government would begin an outreach program through the United Way.

He said the federal government would initiate state-by-state reviews to eliminate roadblocks that may be preventing children eligible for either CHIP or Medicaid from being enrolled.

But governors from both parties defended their records and said they are well ahead of the initial projections for enrolling children in the program. Citing a week-old study by the Kaiser Family Foundation, the governors association issued a fact sheet that said states have enrolled 1.3 million of the estimated 2.6 million eligible children. The governors also asserted that enrollment has risen 55 percent since last December.

"All of us feel we have very good stories to tell about what we're doing," said New Hampshire Gov. Jeanne Shaheen (D), adding, "This is one where I'm going to disagree with the president."

Shaheen complained it had taken her state a year to receive a federal waiver to implement the program without the approval of her legislature. Wisconsin Gov. Tommy R. Thompson (R) said his state had waited 18 months for federal approval of a program far more ambitious than CHIP, one that covers children and their parents. "The president should be pointing at his own administration," he said.

Minnesota Gov. Jesse Ventura (I) said his state had moved earlier and more aggressively than Washington to provide health care coverage for children, but "getting people to apply" remains a problem. "I don't know what to do about that [other than] run around and put hammer locks on them, and I don't have time to do that," Ventura said. "So I think it's a matter for us to get out and continue an education process. . . ."

Maryland Gov. Parris Glendening (D) said Maryland had signed up 52,000 of an estimated 60,000 eligible children, but added, "The president is right. Where the money is available, no child should be without health insurance."

Virginia Gov. James S. Gilmore III (R) called CHIP a "good program as a bridge measure" for children, but said the states and the federal government should do more to provide education and jobs "so they're not bound to a welfare program." He also said "we don't think we need people with green eye-shades and dark glasses" from Washington to determine whether the state is doing an adequate job.

Many governors arrived nervous that some lawmakers in Washington were eyeing surplus welfare funds in the states as a pool of money to fund other programs. But with reassurances from Clinton and Nickles, that concern evaporated. "I thought it came right off the table," Gilmore said.

Staff writers Ellen Nakashima and Eric Pianin contributed to this report from Washington.