This is moving now on Twitter
McConnell: "Highly likely" Senate Intel Committee will look into whether Trump directed Flynn to talk sanctions with Russia ambassador
— Manu Raju (@mkraju) February 14, 2017
So right now the state of play is that the House is not investigating Flynn and it is looking like the Senate will.
The the question becomes what authority does the Senate actually have to do this as conversations between Flynn and Trump are certainly covered by executive privilege. The most likely explanation is that Mitch McConnell is saying whatever he thinks he needs to say to avoid pain and in the end will do what he does best: nothing.