(Adds governors' comments, states' recessions)

By Caren Bohan and Lisa Lambert

WASHINGTON, Feb 23 (Reuters) - U.S. President Barack Obama sought on Monday to bolster political support for the $787 billion economic rescue package, telling the nation's state governors the money would go out quickly and be spent wisely.

The package of public works funds, tax cuts and aid to states that Obama, a Democrat, signed into law last week highlighted partisan division in Washington after it was passed by Congress with only three Republican votes.

Many congressional Republicans derided the stimulus as wasteful. While some Republican governors have said they would refuse part of the money, most state leaders have welcomed it as needed help for their fiscal woes.

Meeting with the governors of both parties at the White House, Obama told them a $15 billion portion of the stimulus package to help states pay for the Medicaid health program for the poor would be going out on Wednesday.

"This is not a blank check," Obama said. "We're going to work with you closely to make sure that this money is spent the way it's supposed to."

Obama pushed the stimulus plan through the Democratic-led Congress, arguing it was needed to prevent the U.S. recession from turning into an economic catastrophe.

But he has been forced to defend the measure as Republicans in Congress, and some governors, characterized it as larded with wasteful spending and warned it would only bloat the budget deficit.