There's no problem with your predicate.
However, I don't understand your subject.
Our resolution should begin at midnight on January 1.
4 answers
The only problem I see (and it has nothing to do with anything dangling!) is whether you mean midnight that begins January 1 or midnight that ends January 1. I think it's the former, right? How else can you prase this?
phrase -- not prase!!
I midnight that begins on January 1st.