Graham, R-S.C., made the claim Wednesday on "Hannity," adding that Democratic lawmakers appear to have a "radical agenda."
"I don't think you can get the Democratic nomination for president without advocating for the impeachment of Donald Trump," Graham said.
"I don't think you're going to be able to survive in the Democratic Party ... if you don't call for Trump's impeachment," he added.
Graham claimed if House Democrats attempt impeachment proceedings, they will ensure Trump's reelection.
But, he said most Democrats will not take Special Counsel Robert Mueller's report as the "final word" on the Russia investigation.
"Trump did not collude with Russia," Graham stated. "The bottom line is the Democrats want an outcome, the Mueller report did not give them the outcome they wanted and they're going to keep going until they get the outcome they want."
Graham projected that in the next wave of elections, "the public is going to kick the Democrats out of power and reelect the president - if he stays focused on doing the job for the American people."
"I think Medicare-for-all means 'Medicare-for-nobody'," he said of a proposal popular with some 2020 Democrats.