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Senate Majority Leader Mitch McConnell said Tuesday that the Senate will address President Trump's request to increase stimulus checks sent to Americans to $2,000, but did not commit to pushing the issue as he blocked attempts by Sen. Bernie Sanders and Senate Minority Leader Chuck Schumer to put the House bill on $2,000 stimulus checks up for quick consideration.

That led Trump to launch a Twitter broadside against Senate Republicans, warning them that if they don't have a "death wish" they'll back the boosted checks. 

Schumer's request would have passed the stimulus checks Tuesday afternoon. Sanders' request would have set a vote on the bill for stimulus checks Wednesday afternoon.

Speaking on the Senate floor, McConnell acknowledged that Trump "would like further direct financial support for American households." He also mentioned that Trump wants Congress to address Section 230 of the Communications Decency Act, which provides protections for companies that host third-party content on their platforms -- like Facebook and Twitter -- and that Trump wants Congress to look into election security.

130 HOUSE REPUBLICANS, 2 DEMOCRATS VOTE AGAINST $2,000 STIMULUS CHECKS

"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."

Notably, McConnell did not promise action on the $2,000 stimulus checks. Whether the Senate even gets to a cloture vote -- a vote to end debate and proceed to a final vote --  on the stimulus checks will be up to McConnell. He controls Senate floor action.

If Trump gets his way, McConnell will bring the checks up for a vote. 

"Unless Republicans have a death wish, and it is also the right thing to do, they must approve the $2000 payments ASAP," Trump tweeted Tuesday. "$600 IS NOT ENOUGH! Also, get rid of Section 230 - Don’t let Big Tech steal our Country, and don’t let the Democrats steal the Presidential Election. Get tough!"

Sanders then objected to McConnell's attempt to quickly move to a vote to override Trump's veto of the National Defense Authorization Act (NDAA).

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"There are only a few days left in this session," Schumer said, urging the Senate to prioritize relief checks. "We should not adjourn until the Senate holds a vote on both measures: the NDAA veto override and the House bill to provide $2,000 checks for the American people."

As of Tuesday afternoon, Sens. Kelly Loeffler, R-Ga.; David Perdue, R-Ga.; Lindsey Graham, R-S.C.; Josh Hawley, R-Mo.; and Marco Rubio, R.-Fla., have backed the House legislation for $2,000 stimulus checks, which passed with more than a two-thirds majority Monday. 

Seven more Senate Republicans would need to come out in support of the checks in order to break a filibuster on a cloture vote and set the issue for an up-or-down vote.  

Sanders' objection to McConnell's attempt to quickly consider the NDAA veto led McConnell to schedule a vote on a motion to proceed on the veto override for Wednesday afternoon. McConnell could file cloture to end debate on the override Wednesday night, which would allow the Senate to take up that cloture vote on Jan. 1. 

This tees up a potential vote on the actual veto override for Saturday, Jan. 2. 

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That puts Congress on a tight timeline on both the veto override and the stimulus checks. The current Congress must adjourn by Jan. 3.

Fox News' Jason Donner contributed to this report.