Do the Senate meeting and the DC sequence connect?

Could be. That would be an interesting scene transition, to put it mildy. Although it's also possible that this takes place earlier in the film before the monster action gets going. Maybe more as a foreshadowing of what is to come later in the film. We'll find out soon enough.

No.

Gmkgoji: Why no? 

I haves the spoilers

Gmkgoji: Wouldn't that ruined your movie watching experience?

Godzillatheking123 

It did. 

Gmkgoji: A shame.

Gmk does not have the spoilers. @Gmkgoji, Please refrain from disputing other members questions without concrete evidence and knowledge of the matter. It derails the topic and cuts the discussion short if they assume you have insider knowledge - of which you do not. So please, instead answer "I don't think so" instead of a definite "no" followed by telling anyone you have access to spoilers. Thank you

Chris

Sorry, I don't have insider knowledge, you are correct. Guess I should not post replies to topics like these

I think it would be hardly, as Dr. Serizawa and other members of Monarch were already on several locations and incidents. Unless Monarch travelling to Antarctica and Mexico and all the events in between took only a few minutes. 

I'm guessing there would already be several hours worth of difference in between Ghidorah's attack and the Senate meeting.