Shumlin, a Democrat, made the comments Thursday, a day after Maine Gov. Paul LePage declared a civil emergency in his state.
LePage said the civil emergency allows him to suspend state laws and regulations to better manage the shutdown's impact on Maine and expedite unemployment benefits for furloughed workers.
Shumlin says none of the nation's governors will be able to do the jobs they've been elected to do if the federal government shutdown continues much longer.
LePage says the shutdown is a result of a failure of leadership in Washington and is encouraging Congress to find a resolution.