Trump is requesting Congress rescind $15.4 billion in spending from previously approved funds, the largest single such request from a White House and the first in nearly two decades.

McConnell's comments, while not a ringing endorsement, are more positive than his reaction to the White House's floated plan of clawing back money from the omnibus.

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The GOP leader shut the door on such an idea last month, telling Fox News: “You can’t make an agreement one month and say: 'OK, we really didn’t mean it.' "

The rescissions plan, according to the White House, would largely target unobligated funds, including money leftover in now defunct accounts.

"I would certainly like to see us move on it," he added.

Congress has 45 days to approve the request in a measure that is not subject to a Senate filibuster. That would allow Republicans to pass a rescissions package without help from Democrats, as long as they can keep most of their fragile 51-seat caucus united.

"I would think it could, yeah. I mean I think if it's reasonable and they're spending issues most Republicans agree with ... it's possible," he said.

John Kennedy John Neely KennedyMORE Sen.(R-La.) noted that he supports the package but thinks "it doesn't go far enough."

"I will be on rescissions like a cat on a fat rat," he added.

No Republican senator has officially come out as a "no" vote, but several noted on Tuesday that they were still reviewing the details of the bill.

"I need to look at the specific accounts. For example if money is taken out of the highway trust fund that doesn't make sense to me on the surface because we're in a situation where the highway trust fund is broke every year and we have to borrow from the general fund," she said.

"I've been a big proponent of CHIP," she said. "I have concerns, but I haven't looked at the full details."

There's no sign Democrats will come on board, though lawmakers up for reelection in red and purple states are likely to come under pressure from the White House.

"I think doing these types of rescissions in the Senate would sour the ability to get [appropriations] done," he added.