"@BarackObama @Eastwood_ Greetings from coal country! Hazard, KY -MM," McConnell tweeted from the campaign's account.

The tweet is accompanied by a photo of the senator sitting at a bar with a beer, gesturing to an empty chair with a glass of wine next to it. The empty chair is an apparent reference to Clint Eastwood's unusual Republican National Convention speech, which he delivered largely to an empty chair meant to represent President Obama.

It's a response to a jab Obama issued at the White House Correspondents' Dinner this weekend. 

“[…Some] folks still don’t think I spend enough time with Congress. ‘Why don’t you get a drink with Mitch McConnellAddison (Mitch) Mitchell McConnellSenate passes 0B defense bill Overnight Health Care: New GOP ObamaCare repeal bill gains momentum Overnight Finance: CBO to release limited analysis of ObamaCare repeal bill | DOJ investigates Equifax stock sales | House weighs tougher rules for banks dealing with North Korea MORE?’ they ask. Really? Why don’t you get a drink with Mitch McConnell?” he said, to laughter from the crowd.

The McConnell campaign has indicated it plans to put particular emphasis on its digital and data efforts going into what could be a tough fight, if Democrats front a credible challenger and place McConnell at the top of their Senate target list, as they've indicated they plan to do.

No Democrat has yet entered the race, however.