WASHINGTON (Reuters) -U.S. Senate Majority Leader Mitch McConnell on Tuesday put off a vote on President Donald Trump’s call to boost COVID-19 relief checks and urged the Senate to override his veto of a defense bill, in a rare challenge to his fellow Republican three weeks before he vacates the White House.McConnell acted shortly after Trump assailed Republican leaders on Twitter, calling them “weak” and “tired” in an apparent effort to get the Senate to increase COVID-19 relief checks to $2,000 from $600 and to support his defense bill veto. After McConnell addressed a rare year-end Senate session, Trump tweeted that the Senate must approve the higher payments as soon as possible, “unless Republicans have a death wish.” McConnell, the top Republican in the Senate, later introduced a bill combining the larger checks with provisions meeting Trump’s demands for a repeal of legal protections for social media companies and a probe of the November election results. An aide described the action as a procedural move in response to a White House request. Senate Democratic leader Chuck Schumer predicted the legislation would never become law. McConnell had said earlier in the day that the Senate would begin to examine the checks along with election integrity and limits on big technology companies: “This week the Senate will begin a process to bring these three priorities into focus.” He also added to the Senate calendar the same stand-alone measure to increase direct payments to $2,000 that the Democratic-led House of Representatives approved on Monday. Republicans in Congress have largely stuck with Trump through four turbulent years but he is angry that his party’s lawmakers have not fully backed his false claims of fraud in his November election loss to President-elect Joe Biden. The president has also chafed at the Republicans’ efforts to override a presidential veto for the first time since he took office in 2016 and their opposition to bigger aid checks. With the New Year’s Day holiday on Friday and a new Congress due to be sworn into office on Sunday, the current crop of lawmakers have only a short time to act. A combined $892 billion bipartisan coronavirus relief package and $1.4 trillion spending bill that Trump signed into law on Sunday contains $600 checks for people hit hard financially by the coronavirus. Democrats believe the stimulus check issue could give them an advantage in two critical Georgia runoff elections next week that will determine which party controls the U.S. Senate and the fate of Biden’s agenda when he takes office on Jan. 20. U.S. stocks dipped into negative territory after McConnell rejected Schumer’s call for the Senate to approve the increased stimulus aid by unanimous consent. McConnell refused to cave to Trump’s demands on the military bill and set the stage for a vote to override the veto in the coming days. “For the brave men and women of the United States armed forces, failure is simply not an option,” he said. “So when it’s our turn in Congress to have their backs, failure is not an option either. I would urge my colleagues to support this legislation one more time.” Slideshow ( 3 images ) Overturning Trump’s veto requires votes by two-thirds of the House and Senate. The House overrode Trump’s veto on Monday. If the Senate seconds the House action, the defense bill becomes law. It would be the first veto override of Trump’s presidency. The Senate is expected to hold a procedural vote on Trump’s veto on Wednesday evening, which could lead to final passage later in the week or over In a tweet storm just before the Senate session started, Trump attacked “weak and tired” Republican leaders. “WE NEED NEW & ENERGETIC REPUBLICAN LEADERSHIP,” he wrote in a tweet falsely claiming that voter fraud caused his defeat in the Nov. 3 election. “Republican leadership only wants the path of least resistance. Our leaders (not me, of course!) are pathetic. They only know how to lose!” he wrote without mentioning any party leader by name. Final passage of the COVID-19 aid increase in the Senate would require 60 votes including the backing of a dozen Republicans. At least five Republicans have so far voiced support for the higher payments. They include Republican Senators David Purdue and Kelly Loeffler, who are candidates in the Georgia runoffs on Jan. 5.