I wouldn't worry about House.
I think if someone should question something, then it should be Cuddy.
None of her relationships worked, cause, let's face it, she is weak when it comes to that.
She always wants to skip the lovey dovey part and make it complicated, and eventually just end it.

I somehow already see her screwing this with House up.
Just like being stubborn about him lying to her seems like a 'let's end it already before I get so worked up over it' thing

Hm. Never thought of it that way, Hilly, but I actually agree with you. I think she doesn't realize that she might also pose a threat to the relationship with her constant "You have to do everything right and it cannot ever be just fun"-attitude.

Still, I guess if I were her, convinced that my views are right and the rules I make should be followed and, just for example, that House HAD to apologize, I'd be worried about him self-sabotaging it. Usually one doesn't realize they have to back down - not even Cuddy.

Also, it would kinda be in House's nature to self-sabotage it - maybe even inadvertently.

I think its actually all of the above. They both worry a lot about everything. Which is normal i would think...