(CNN) The White House and GOP senators are in the midst of a last ditch scramble to save President Donald Trump from an embarrassing defeat -- and Republicans from the political backlash of turning on the President.

A group of GOP senators is pushing a proposal that would limit future National Emergency Declarations, and are seeking a commitment that the President would publicly support it, in exchange for dropping their opposition to the current national emergency. The White House, so far, has declined to provide that commitment.

Bottom line: The effort to reach an agreement has fallen short up to this point, and all signs still point to major defections come Thursday's vote. Just about everyone in the GOP conference is behind a proposal from Sens. Mike Lee and Thom Tillis, aides say, so if the White House comes around to it, it could be significant. But the White House counsel's office, congressional aides say, has been skeptical to outright opposed. And there is zero indication, at least at the moment, Trump will come on board.

Reality check: "There's really no way out of this," one GOP senator, skeptical of the talks between the White House and Republican senators, told CNN on Tuesday night. The way this likely ends, the senator said, is the Senate votes on Thursday on the resolution of disapproval and GOP losses are around what we've been reporting for the last few weeks -- somewhere between 10 and 15 Republicans.

The context here is that the proposal, led by Lee and Tillis, would move to limit executive authority on national emergencies. That is something, this senator said, "no White House counsel would ever agree to."

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