Washington ? The nation’s governors, whose state budgets have been battered by recession and rising expenditures for homeland security and Medicaid, opened their winter meeting here Saturday with a plea for help from Washington.

Michigan Gov. John Engler, chairman of the National Governors Assn., said the cumulative shortfall in state budgets, estimated at more than $40 billion, was far worse than states experienced during the more severe recession of a decade ago.

The shortfall has forced governors and legislatures to cut spending and in some cases to raise taxes. “We’re dealing with these problems,” the Republican Engler said, but added that “the consequences of this $40 billion problem could be eased or maybe even alleviated here in Washington.”

The governors arrived with a lengthy agenda for President Bush and Congress and will press their case over the next three days, including a Monday afternoon meeting at the White House with Bush.

On homeland security, the governors said Saturday they were pleased with the funds for the states in the president’s new budget. But they are concerned that in the future Washington will order costly improvements without offsetting funding, that overlapping federal authority will bring conflicting demands, or that Congress may bypass the states and deal directly with local communities. The governors will raise these issues with Homeland Security Director Tom Ridge, a former governor of Pennsylvania.

The rest of the governors’ agenda includes opposition to proposed cuts in federal highway funding, an appeal for financial assistance for rising Medicaid costs and a new policy statement on welfare, which Congress must reauthorize this year.

Kentucky Gov. Paul Patton, the association’s vice chairman, said Medicaid is the greatest long-term fiscal challenge facing the states, with annual costs growing at more than 10 percent a year, fueled by what he said were “out of control” increases in the cost of prescription drugs.

“When the economy was stronger, states were able to pay for Medicaid, even though it was a stretch,” Patton said. “We can no longer afford Medicaid the way the benefits package is structured today.”

The governors acknowledged that Medicaid reform was not on the agenda of either the president or Congress this year but warned that restructuring Medicaid was at least as urgent as reforming Medicare. Some governors said immediate help was vital.

On welfare reform, which Congress must reauthorize for the first time since enacting dramatic changes in the program in 1996, the governors want federal spending increased, despite a sharp decline in welfare rolls, arguing that inflation has eroded the value of the federal block grant to the states.

“I think we would all agree that welfare reform worked very well in a strong, improving economy,” Patton said. “I think our challenge now is to see how it’s going to work in a deteriorating economy.”

Engler said the request for more federal welfare funding was not a change in thinking among governors, who agreed in the mid-1990s to accept less money in return for greater flexibility. He said the federal government has chipped away at that flexibility. “I think we’ve kept our deals,” he said. “Washington hasn’t been as consistent.”

Patton said highway funding ranks at the top of the governors’ agenda because of a proposed cut of about $8.6 billion, a reduction of about 25 percent in the program for states. If that stands, Patton said, it will be “an absolute disaster” for the states.