The shift comes as the state of the economy grows worse and more GOP senators call for action. But Senate Majority Leader Mitch McConnell (R-Ky.) is already making clear Republicans will not support an extension of the extra unemployment benefits Congress passed in March. GOP lawmakers say the additional aid — which expires at the end of July — provides a disincentive to return to work and some are now proposing alternatives they can rally behind.

Democrats counter that Congress must extend benefits for the millions struggling to pay bills as the U.S. faces its most uncertain economic climate in generations. Regular unemployment insurance, they note, covers just half of workers’ pay on average.

In fact, some top Democrats want to go further. Senate Minority Leader Chuck Schumer (D-N.Y.) is eyeing a push to automatically tie unemployment benefits to the condition of the economy, according to a Senate aide — a move that has not been previously reported. Supporters of the automatic stabilizer idea, which Speaker Nancy Pelosi has also publicly endorsed, say it would avoid the political wrangling that could otherwise threaten to hold up much-needed aid.