ABC News' Michael Falcone rpeorts:

Who wants to get a drink with Mitch McConnell?

On Monday, the senator's campaign account tweeted this photo of him, apparently at a bar in Kentucky, seated with a beer next to an empty chair and a glass of red wine. The tweet is addressed to both President Obama and Clint Eastwood (also of empty chair fame).

@ barackobama @ eastwood_ Greetings from coal country! Hazard, KY -MM twitter.com/Team_Mitch/sta…

— Team Mitch (@Team_Mitch) April 29, 2013

This, of course, is McConnell's way of responding to the president's jokes over the weekend at the White House Correspondents Association dinner made at McConnell's expense.

"Recently, I had dinner - it's been well publicized - I had dinner with a number of the Republican senators," Obama said. "And I'll admit it wasn't easy. I proposed a toast. It died in committee.

"Of course, even after I've done all this, some folks still don't think I spend enough time with Congress. " he added. "'Why don't you get a drink with Mitch McConnell?' they ask. Really? Why don't you get a drink with Mitch McConnell? "

So was McConnell's joke about the joke actually an invitation to clink glasses with the Kentucky senator?

"I'm shocked. He's obviously not seeing my soft side," McConnell said of the president's ribbing on Monday at the Southeast Kentucky Chamber of Commerce, according to the Washington Post's Karen Tumulty and Sean Sullivan.