mixing cream cheese and butter

It sounds like you under beat them. You can mix both the cream cheese and the butter together (as you stated at room temperature). I always do. The key is to cream them together before adding other ingredients. This will make sure that your cheesecake is smooth.

When making a cheesecake I nearly always mix the cream cheese at a LOW speed for a couple minutes, scrape, mix for another minute at low, stream in the sugar while its mixing and mix for another couple minutes...at low. Having patience can sometimes pay off. You don't want to beat a cheesecake filling on medium or high speed because you'll wind up with a lot of air in the batter and it will souffle in the oven...leading to cracks. I would try mixing the cream cheese until its smooth. Scrape that bowl. You could even do it by hand at first to make sure nothing gets stuck to the bowl. That's how I always get lumps, some cream cheese was stuck to the side and when I get ready to pour the filling into the crust, it gets loosened at forms lumps. After the cream cheese is smooth, while its mixing, add the butter in small pieces and wait for it to incorporate. I'd caution against microwaving either, because most recipes that call for whole cream cheese or butter are doing so because its important that they keep their air. Microwaving them invariable causes some collapsing of that structure. It would work in a pinch and if you're VERY careful, but there are other ways.

Butter is a strange ingredient in a cheesecake filling. Is the recipe something you're tied to? Because I'd consider a recipe that doesn't require emulsifying those two ingredients. I've never thought while eating a traditional NY cheesecake recipe "this could use the addition of butter". If its the best thing you've ever tasted, I'd say go for it, and let us know!

It does sound like under-beating. What was the ambient temperature of the kitchen? Sounds like it might have been a bit more on the cool side. I find that warming the cream cheese just a tad can help it combine better with butter that is soft (but not melted). Definitely try beating up the cream cheese first, then add the butter and keep betting until the mixture is smooth.

I recently made a cookie dough that had both cream cheese and butter. I warmed the cream cheese in the microwave for ~20 seconds and beat it together with softened butter in a stand mixer. No lumps.