I'm doing a "House Always Wins" play through. At what point do I start pissing off the NCR as well as the Legion? Do I have to contend with two sets of hit-squads on a daily basis?

I've completed "House Always Wins Part II". Currently my NCR reputation is "Idolized".

Both House and NCR want me to go talk to the Boomers. I'm guessing if I get them to side with House the NCR is going to be a bit miffed.

Time to stock up on stimpaks?

Actually you shouldn't. If you do a House play-through, you can maintain good relations with the NCR as long as you don't purposely piss them off. Doing a couple side jobs for groups like Crimson Caravan (gaining some NCR favor) can help maintain that too.

In fact, a good reputation with the NCR is required to do one of House's later quests successfully.

As I understand it, the Legion and the NCR only send hit squads after you if your reputation is negative. If you have neutral or positive rep, you don't get hit squads. Now, as has been stated, you can go through House's quest line without getting the NCR mad, but you will get the Legion mad at you. However, if you take the time to get your reputation with the Legion up to Idolized before you start doing things that make them mad, the lowest your reputation will go is Wild Child, which is considered neutral, not negative. That means no hit squads.