WASHINGTON — A stalemate over an emergency infusion of cash to help small businesses battered by the coronavirus pandemic intensified on Monday after Democratic leaders doubled down on demands for additional money for state and local governments, hospitals, food assistance and rapid testing.

With Speaker Nancy Pelosi of California and Senator Chuck Schumer of New York, the minority leader, insisting on adding to the Trump administration’s request to inject $250 billion into the loan program, it is unclear whether lawmakers can reach a consensus this week even as officials warn that the program could run out of funds as early as Friday.

The impasse over what was intended to be an interim emergency package before another broader stimulus deal comes as businesses say they have yet to receive a majority of the billions slated for the program. The National Governors Association also called on Saturday for Congress to allocate an additional $500 billion to states to help offset state revenue shortfalls, more than double what Democrats initially demanded.

“We have real problems facing this country, and it’s time for the Republicans to quit the political posturing by proposing bills they know will not pass either chamber and get serious and work with us toward a solution,” Ms. Pelosi and Mr. Schumer said in a joint statement.