Aides aren't completely ruling out the possibility of breaking the stalemate and pulling together a deal by early Thursday.

Republicans made a new offer to Democrats on Wednesday evening, but also warned that attempts by Democrats to include any new immigration restrictions would be counterproductive to the chances of a deal.

Leahy on Wednesday night pointed to the House as the hold up on getting a disaster aid deal done this week, arguing that he and Shelby were ready to move on a bill.

"We're ready to go," he said, "but the House is not ready to move."

A House Democratic aide said that they would respond to the GOP offer on Wednesday night. But they also shot down a meeting between the top four appropriators, arguing that they weren't interested in "photo op meetings."

"We don’t have any meetings scheduled. We are carefully considering the GOP offer that we received in the last hour and a half," the aide said. "Instead of photo op meetings, we want to iron out the remaining details and get this done."