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Senate Majority Leader Mitch McConnell on Tuesday introduced his own version of a bill to increase the $600 stimulus checks from the coronavirus relief package to $2,000, but also included two other major priorities for President Trump.

The legislation would also repeal Section 230, the controversial liability protection for online platforms, and create a committee on the Election Assistance Commission to study election integrity. 

McConnell set the table for a bill to address these three issues in his floor remarks Tuesday. 

"During this process, the president highlighted three additional issues of national significance he would like to see Congress tackle together," McConnell said, before listing off the president's grievances about the amount of the stimulus payment, Section 230 and the election. 

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"Those are the three important subjects the president has linked together," McConnell said. "This week, the Senate will begin a process to bring these three priorities into focus."

The remarks were not a firm promise that any of these issues would receive a vote or that McConnell would push particularly hard for them. And McConnell's bill itself is unlikely to gain the support of the 60 senators that would be needed to break a filibuster. Some Republicans, especially the handful who have already said they favor $2,000 stimulus checks, would likely back the bill, but most Democrats probably will not vote for it due to the other issues McConnell's bill addresses. 

What McConnell's bill could do, however, is allow GOP senators who want to be able to say they voted for $2,000 stimulus checks to do so while protecting priorities of the majority of his caucus which has previously opposed the checks. 

Sen. David Perdue. R-Ga., one of the Republicans who has said he supports $2,000 checks -- and is also in a fierce runoff set for Jan. 5 to hold onto his seat -- said on "Fox & Friends" Wednesday that he supports the McConnell bill. 

"The Democrats themselves held this up for months and so here in the last minute, they're complaining about the normal operation of the Senate," Perdue said. "I'm an outsider of this process but I can tell you these things that Mitch McConnell is trying to do are in line with what the President has said. I support what the President is trying to do relative to Section 230, the repeal of that and also the $2,000 stimulus checks. We're in full support of that."

Senate Minority Leader Chuck Schumer, D-N.Y., called McConnell's proposal a "cynical gambit."

No action on McConnell's bill has been scheduled. Trump, meanwhile, warned Republicans that they should support quick delivery of stimulus checks unless they "have a death wish" in a Tuesday tweet. He doubled down Wednesday morning, saying, "$2000 ASAP!"

McConnell on Tuesday blocked attempts by Schumer and Sen. Bernie Sanders, I-Vt., to quickly pass the House bill on stimulus checks which cleared the lower chamber with more than two-thirds of members voting in favor of it Monday. 

Whether either the House bill or the McConnell bill even receive votes will be up to McConnell, who controls the action on the floor. The majority leader is currently prioritizing efforts to override Trump's veto of the National Defense Authorization Act (NDAA), which funds the military for the next year. 

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Trump objected to the fact that the bill renamed bases named after Confederates and did not repeal Section 230, but the legislation passed overwhelmingly in both the House and the Senate. The House has already voted to override the president's veto. 

Sanders has delayed McConnell's efforts on the defense bill in an attempt to extract concessions on the stimulus checks. But if McConnell forges ahead as scheduled, there could be a vote to end debate on the veto override on Friday and a final vote to override the veto on Saturday. 

The current Congress ends on Sunday, Jan. 3, which means that any other action on stimulus checks must happen quickly. At that point, lawmakers will have to completely restart the legislative process. 

Fox News' Jason Donner contributed to this report.