Sources on and off Capitol Hill said Reid wants to swap out the bill's current rack of "pay-fors," and replace them with a package including a surtax of 5 percent on millionaires.

Details remained scarce late Tuesday, but earlier Reid hinted at such a move. Speaking to reporters just off the Senate floor, the Nevada Democrat said the Senate would vote on President Obama's jobs bill in the coming weeks, but only after Democrats find new ways to pay for the package.

"There is a wide range of things we're looking at, because the only objections I heard from my caucus is dealing with the pay-fors," he said. "So, we're resolving that issue as we speak."