Governors from both parties appealed yesterday for the Bush administration and Congress to provide more money for a health-care program that insures millions of children.

At stake is coverage for 6 million people, overwhelmingly children, as well as the hopes of many governors in tackling the challenge of uninsured working families.

"We can come to a consensus that children should be the first priority," Georgia Gov. Sonny Perdue (R) said.

State leaders met privately to discuss the State Children's Health Insurance Program at the annual winter meeting of the National Governors Association.

"This is one area where I think people stand entirely together," said New Jersey Gov. Jon S. Corzine (D).

Georgia and New Jersey are among 14 states expected to run out of money for the program before the next budget year begins in October, In Georgia, a shortfall could happen as soon as March.

The governors want two things: enough money -- estimated at $745 million -- to keep the program float through October, and changes to President Bush's budget. Analysts say the president's spending plan would shortchange the program even if the number of people served does not grow.

Health and Human Services Secretary Mike Leavitt said he met privately with the governors but offered little hope that the administration will accept their demands.

Last night, Bush welcomed the governors to a formal dinner at the White House. "I believe governors add a lot to the work of our nation," he said. "I believe if we work together we can do a lot of good things."

The insurance program, approved in 1997, covers uninsured children whose families earn too much to qualify for Medicaid. More than a dozen states have expanded the program, which also insures about 639,000 adults.

Many governors said administration attempts to curb the program would undermine state efforts to offer universal health-care plans.

Leavitt said yesterday that there is enough money among states to cover short-term shortfalls in the program, if states with surpluses share with those with deficits -- an idea that has little support among governors. And Bush wants the program to remain focused on poor children, not all children and not adults, Leavitt said.

Maryland Gov. Martin O'Malley (D) said that during their private lunch, many governors were "visibly frustrated" by the administration's approach.

Arizona Gov. Janet Napolitano (D), who heads the association, said the issue will come up today when governors meet with members of Bush's Cabinet.

Amid the talk about dollars and percentages, the real cost is being ignored, some governors said.

"I think more about what it means to be a parent, a parent who can't go to sleep at night without worrying that 'if my kid gets ill tomorrow or gets in an accident, he won't have adequate coverage,' " Virginia Gov. Timothy M. Kaine (D) said. "I can't imagine more anxiety."