Minnesota Gov. Tim Pawlenty, a potential GOP presidential candidate, stepped up his attack Thursday on President Barack Obama's federal health care law with a court filing challenging its cost to states.

Pawlenty and Rhode Island Gov. Donald Carcieri, both Republicans leaving office soon, joined in the federal court filing in Pensacola, Fla.

A judge there ruled last month that parts of a lawsuit filed by 20 other states challenging the health care overhaul can go to trial. The two governors' filing seeks permission to submit a friend-of-the-court brief in support of the lawsuit.

The filing, written by a Washington lawyer from the Competitive Enterprise Institute, said the governors are safeguarding their citizens from "federal abuse of the spending power." They argue the law places liabilities on states through a Medicaid expansion.

"Although the Act indicates that the federal government will initially pay for some Medicaid expansions, the states are advised that they will pay for 10 percent of some unspecified costs in four years, and there is no indication that the states will not pay more in succeeding periods," the governors' document said.

Pawlenty has been vocal in his opposition to the law. He has said he would make repealing it a focal point of a run for president in 2012 if he wages a campaign. Pawlenty has ordered state agencies to avoid discretionary grants related to the health law.