I am a little confused. My spouse just asked me if I was done working for the day because he wanted to have some fun. But as far as I know, I can't do anything with him other than just talk to him and kiss him. Is this just one of the things he's supposed to say or am I missing something?
That is just one of the possible dialogues that spouses will say, and its only purpose is to give flavour to marriage, hinting at what happens after you go to "sleep".
So no, it has no gameplay effect.
I believe that is some kind of warning message that you will need to protect the marriage to avoid unhappiness. So you continue speaking to your spouse regularly, and kissing and giving him gifts. Normally if you don't protect it the character sits and does nothing or sends weird messages. Not sure if that has been happening to you.