Blackburn is running to hold on to the seat of the retiring Sen. Bob Corker of Tennessee; if Democrats are going to have a chance to win back the Senate, the Volunteer State is one of the key races for them on Election Day.
As for the Kavanaugh nomination - it is officially pending on the floor of the U.S. Senate, but Senate Majority Leader Mitch McConnell has not indicated when he would push to hold a vote.
Sen. Jeff Flake (R-AZ), along with Sen. Lisa Murkowski (R-AK), and Sen. Susan Collins (R-ME) are seen as the holdouts at this point, as Flake and Murkowski have both said more review is needed by the FBI on certain allegations related to Judge Kavanaugh.
Flake is taking flak from both parties on this - from Republicans who feel he is undermining the President, to Democrats worried that the retiring Senator is all talk - and no action.
The President's campaign trip to Tennessee also coincides with the first Monday in October - as the Supreme Court will convene for its new term - with an empty seat on the bench.
The last time the Court was without a full complement of justices was after the death of Justice Antonin Scalia in February of 2016 - Republicans in the Senate refused to hold a hearing on President Obama's nominee, Merrick Garland, ultimately holding the seat open for President Trump, allowing him to place Justice Neil Gorsuch on the bench.
If Kavanaugh's nomination is derailed - the November elections for U.S. Senate could turn into a flash point over whether the President will face a Senate controlled by Democrats, who would be free to reject his Supreme Court choices.