How do you think Mr. House would react to the Courier nuking both the NCR and Caesar's Legion?

The reason I ask is because I'm about to create a brand new character who is going to ally with House and follow all his main quests to the ending. I like to write and roleplay a history for each of my characters, and this particular one will believe in House's ideals to the point where they want to see the NCR and Legion weakened enough so that House can continue to rule the Mojave uncontested. However, if nuking both the factions would actually get House's disapproval (much like he actually doesn't want the Courier to kill Caesar), they wouldn't do it.

Yes, I'm aware that House doesn't actually acknowledge the Courier's actions at all outside of the Lonesome Road DLC. Let's just pretend for a moment that he actually does.

House relies upon the NCR for their economic activity. The Hoover Dam occupation ensures a steady stream of customers, and IIRC he was looking at way to try and expand its attraction as a tourist destination to NCR-ers. Anything that puts this at risk, making the trip more perilous isn't likely to be seen to well by house.

As the strike doesn't immediately effect Ceasar's ability to project a force around the dam, the NCR still has to keep up the same presence; but a weaker Ceasar long term is in his best interest, as Ceasar isn't likely to let a place like Vegas survive (or at least, survive as vegas - Drinking, Gambling, Drugs, six...) so House is likely to be happy with this bit.

For as nuking both - I think he would be quite displeased because of the NCR effect. He's probably be quietly thankful about Ceasar being weakened, but probably not enough to balance the NCR damage.