I think it's a bit early to me thinking about leaving him and all this stuff about drawing a line in the sand seems a it useless. He has said how he feels...he can't help that.
Thee's a saying about marriage being about falling in love with the same person many times and I think that is true. Things can come along and give you blows, stress (as LEM said) can play havic with how you feel about life in general and thus makes you feel less satisfied, happy and open to feeling "love" and the trick I think is to try and get the feeling back.
In your situation, I would "hold my shit" and ask him to come out to dinner. I would tell him that if there is an OW, now is the first, last and only opportunity to come clean about it. If he continues to say there is not, explain to him that couples fall in and out of love many times in many marriages and that there is an element of work to be done to keep you feeling that way.
I would start by trying to reduce stress in your lives. It messes up marriages.
Secondly I would buy a book called "His Needs, Her Needs" and read it together. The number one reason people "fall out of love" is because their needs aren't being met.
Thirdly I would schedule some date time, alone time, reconnection time.
Counselling might also be good but from my experience a crappy counsellor can sometimes make things worse. Chat with them all on the phone or meet in person before going with your DH.
I know you feel hurt, angry and rejected but your DH is telling you how he feels. I don't think this is an insult to you. I think rocky times are part of any marriage and if you can get over this hump then you may well end up with a richer, deeper experience. He is communicating with you - listen to him.
If of course there is an OW, he might well lie. He might lie very convincingly. I have to give this advice, but to save yourself anguish later I'd really look into that possibility.