By Donald Judd, CNN

(CNN) -- Republican Sens. Kelly Loeffler and David Perdue are on defense just under one week from a crucial Senate runoff election that will determine who holds Senate power, as the President's public statements and actions in the final days of his administration are looming over close runoff elections in Georgia.

Among several false claims about election fraud, President Donald Trump called on Georgia Gov. Brian Kemp to "resign from office" in a tweet Wednesday morning.

"He is an obstructionist who refuses to admit that we won Georgia, BIG!," Trump falsely claimed in his tweet criticizing the Republican governor.

Neither senator has commented on Trump's call for Kemp to resign, the latest in a string of incendiary comments the President has made that the two senators -- who have staked their elections on tying themselves to Trump -- have been asked about. The issue is the latest example of the President's unpredictable nature upsetting the race in Georgia, a state President-elect Joe Biden carried in the November election.

The senators have also not commented on if they intend to vote to override the President's veto of the National Defense Authorization Act over a provision that would call for renaming bases named for Confederate generals.

Pressed by Fox News on Tuesday, Loeffler would only say, "I have been proud to support our men and women in the military," calling the President "a huge champion for our military."

Both Loeffler and Perdue have attempted to avoid actively rebutting the President's claims, with Loeffler refusing to comment on if she supported Trump's claims of a rigged election during a debate earlier this month, instead telling moderators, when pressed, "It's very clear that there were issues in this election." For his part, Perdue has also refused to condemn the President over baseless conspiracy theories, telling supporters on the campaign trail in Forsyth, Georgia, that if Democrats win in January's runoff contests and "if they get the White House, then the vice president is the tiebreaker," in any Senate deadlocks.

The tightrope both senators are being forced to walk was also on display Tuesday, as both senators announced they'd back Trump's call for $2,000 in direct Covid relief checks, but stopped short of calling for a vote on a comparable bill that passed the House, even as Senate Majority Leader Mitch McConnell blocked an effort to quickly pass the measure by Senate Democrats and signaled his intent to tie relief to "poison pill" proposals repealing Section 230 and forming an election fraud task force.

Trump's call for $2,000 in Covid relief took Republicans by surprise last week when, after a $900 billion Covid relief package with $600 in direct checks passed both the Senate and the House, the President announced in a video posted online he would not support the bill headed to his signing desk. Trump ultimately signed the bill while vacationing in Florida on Sunday, after an intense lobbying campaign from Perdue, but has maintained his call for $2,000 checks.

Asked Tuesday, Loeffler told CNN, "I've said I've supported (increased Covid relief), I support it. Look, we have to provide relief to Americans," but offered no insight into whether she'd return to Washington to vote on the issue. Perdue ignored multiple requests for comment about whether he'd call on McConnell to bring a vote to the Senate floor while campaigning across the state Tuesday.