The White House acknowledges that yes, governors control how stimulus funds are used in their states, not state legislatures:
In an important victory for the nation’s governors, the White House is acknowledging that state legislatures across the country can’t wrest control of $48.6 billion made available under the new federal stimulus law to help states cope with their budgets.
White House budget chief Peter Orszag says there is no provision in the stimulus law for state lawmakers to accept that money without approval by the governor. South Carolina’s Republican governor, Mark Sanford, has said he may decline more than $700 million in stimulus money because the White House won’t let him spend the money to pay down his state’s debt.
Orszag wrote in a letter to Sen. Lindsey Graham, R-S.C., that Sanford controls those purse strings. The White House also urged Congress to change the law to avoid what it called unfortunate and unintended consequences.