Apart from the complications of Rhode Island law, as a matter of political theory, this strikes me as a reasonable argument:

The lawsuit [by the city of Woonsocket], which also names State Controller Marc A. Leonetti and General Treasurer Frank T. Caprio as defendants, said the money [that the state was supposed to give towns for automobile excise taxes] was appropriated by a legislative act of the General Assembly and that means Carcieri, Leonetti and Caprio have “a clear legal duty” to pay it.
“He may submit the budget, but he does not have the authority under the state Constitution or state law unilaterally to change the General Assembly’s budget after it has passed,” [Woonsocket Mayor Leo] Fontaine said.

I’ve long been including, among my complaints against Governor Carcieri, that he is far too passive about describing the ownership of the budget. Even though we’re into the second month of the calendar year — and the legislative session — legislators have yet to act on the supplemental budget. So, the governor should pay out whatever money is due, to whomever it’s due, until the money runs out and then just shut down. “I’m bound by law to follow the General Assembly’s budgeting,” he could say, “and they’ve chosen to spend the account dry rather than take corrective action.” It’s their responsibility.
WPRI’s recent poll data gives reason to hope that the public is coming around to an understanding of the political dynamics, in this state. Overall, 53% of Rhode Islanders blame the GA for the budget crisis, with another 25% splitting blame between the legislature and the executive. Perhaps based on relative degrees of attention, the General Assembly fares worse as the age of the respondent goes up. Moreover, 61% of respondents want cuts in spending and services and not in taxes.
If increasing understanding is to translate into the appropriate electoral actions — rather than merely contributing to the general grumble — the governor must make the necessary political decisions crystal clear. He should declare that the General Assembly’s failure to act has been an open window next to the budgetary house of cards and then get out of the way of the inevitable.