In an early-morning tweet, Mr Trump shared a news article that featured comments by his supporters criticising the Kentucky lawmaker, who on Tuesday night said the “electoral college has spoken” as it recognised Mr Biden’s win.
One of the comments in the piece, re-tweeted by the outgoing president, 74, questions Alabama-born Mr McConnell’s allegiance to the United States of America.
“Mitch McConnell, @senatemajldr is NOT a Patriot,” reads one of the comments. “Ask his wife. She knows,” it adds, before going on to claim that the 78-year-old lawmaker is “willing to sell America to get what he wants”.
Mr McConnell’s wife, Elaine Chao, is a 67-year-old American politician who serves as US transportation secretary. She was born in Taipei, Taiwan and immigrated to America as a young girl.
The president in his post, which as of Wednesday morning had been shared 17,000 times and liked by over 60,000 Twitter accounts, told Mr McConnell it is “too soon to give up” on the election.
Mr Trump continues to insist, without evidence, that he won the 3 November poll, despite losing the EC and popular vote to Mr Biden, who secured some 80 million ballots in a record year for turnout.
He and his legal team allege that widespread voter fraud took place at the election, but have yet to present any evidence. Team Trump has suffered a raft of legal defeats – including in the Supreme Court – aimed at overturning the results in key battleground states.
Some Trump insiders had previously suggested the EC vote on 14 December could mark the beginning of the end of the president’s desperate bid to hang onto power.
And the vote appears to have marked a shift in the Republican Party’s willingness to continue humouring the defeated incumbent and his false claims that the election was “stolen”.
Some congressional Republicans, who had for weeks refused to acknowledge Mr Biden as president, are now publicly recognising his win.
Mr McConnell joined his No 2 in the Senate, John Thune, in congratulating Mr Biden on his win. “It’s time for everybody to move on,” the South Dakota lawmaker said.
Despite apparently dwindling support among the GOP’s top brass, Mr Trump still commands the support of a substantial number of House Representatives and some senators who benefited from Trump votes at the elections.
Nearly two-thirds of House Republicans backed a Trump lawsuit filed in Texas earlier asking officials there not to recognise Mr Biden’s wins in Michigan, Pennsylvania, Georgia and Wisconsin.
Although the Supreme Court last week threw out the case, the 120 lawmakers that supported it underlines the president’s continuing influence over the party.
Mr Trump, who some have suggested could act as a “shadow president” throughout the next four years, secured the votes of almost half the US electorate at the election.
And the president has in recent weeks repeatedly reminded GOP lawmakers who have spoken out against him about that increased vote share.
“Mitch, 75,000,000 VOTES, a record for a sitting President (by a lot),” Mr Trump wrote in the Wednesday morning tweet. “Too soon to give up. Republican Party must finally learn to fight. People are angry!” he added.
Despite running out of road, team Trump is continuing to insisit it will contest the election results.
As Republicans began discussing a Biden presidency more openly, Mr Trump pledged to press forward with almost nonexistent legal options.
“Tremendous evidence pouring in on voter fraud. There has never been anything like this in our Country!” Mr Trump tweeted just as members of his party were publicly recognising Mr Biden’s victory.