Senate GOP Leader Mitch McConnell, R-Ky., pulled the trigger on a Republican effort to repeal the Patient Protection and Affordable Care Act on Tuesday, this coming just one day after a federal district court judge declared the health care law's individual mandate unconstitutional.

McConnell introduced the House-passed repeal legislation as an amendment to the pending Federal Aviation Administration bill now before the Senate.

Leadership aides, both Democratic and Republican, tell Fox a repeal-related vote is expected on Wednesday.

Democrats made a slight shift in their effort to combat the GOP repeal effort, by saying Republicans are taking their eye off the jobs ball. Sen. Chuck Schumer, D-Ny., accused Republicans of "not focusing on the average voter."

But McConnell fired back on that same front.

"Employers big and small have been desperately trying to get the message across of how damaging this bill will be to their ability to create jobs. They tell us the impact of this bill is severe," McConnell said, as he called on Democrats to "reevaluate your vote."

Senate Majority Leader Harry Reid, D-Nev., decried GOP efforts at repeal on Tuesday, telling reporters, "It's not going to go any place. It's a deficit buster, to say the least."

Indeed, the nonpartisan Congressional Budget Office has estimated that repealing the health care law will result in a 10 year increase to the deficit of $230 billion.

Republicans have repudiated the CBO analysis, saying that only in Washington can not paying for something result in a deficit increase.

The repeal effort, GOP aides concede, is expected to fail. Republicans occupy just 47 seats in the chamber, well short of the 60 needed to break any filibuster, and though Reid would not predict that every Democrat would oppose repeal, it is clear McConnell will not be able to muster the 60 votes necessary to overcome Democratic objections.

But this expected failure at repeal would represent merely the beginning of GOP efforts to scrap or make major changes to the health care law. Senate Finance Committee Chairman Orrin Hatch, R-Utah, has introduced a handful of measures that either eliminate the mandates or strike at the heart of a major funding stream. Sens. Lindsey Graham, R-SC, and John Barrasso, R-Wyo., a physician, also introduced a measure Tuesday that allows states to opt out of the mandates in the law, a move that the duo readily conceded was designed to kill the bill.

Meanwhile, FOX News has learned that a handful of Senate Democrats are working behind the scenes at possibly removing the mandate. Sens. Ben Nelson, D-Neb., and Claire McCaskill, D-Mo., are among those trying to figure out whether or not the mandate can be removed and replaced with a limited, national open enrollment period where Americans would be heavily penalized should they opt to purchase insurance at a later date.

"We are exploring whether or not it's possible to get enough more [sic] people into the pool by limiting the enrollment time and having significant financial penalties if you don't sign up during the enrollment time, similar to what happens now," McCaskill said.