There’s a question: how far into the broken United States could a hostile Canada or Mexico get before it received serious opposition?
Yeah, since the OP specified contiguous states, adding Nevada and another state sounds good.
I would have wanted the three west coast states plus Alaska and Hawaii, but they technically aren’t contiguous.
Why does this remind me so much of No Truce with Kings?
You’re not alone. The Pacific States is kinda what I had in mind when I made my earlier comment.
I’ll take the mid-Atlantic: NY, NJ, PA, MD, VA. I figure we don’t need Delaware that badly.
ETA: Also, hi Midwesterners, we control one bank of the St. Lawrence for a pretty good stretch. Just sayin’.
What could be done is take six states, then use it as a bargaining chip.
Doesn’t it have a ton of metals used in industry? Or am I mistaken?
Blackjack and hookers.
I think armies tend to attract enough of those without needing to take over Las Vegas. 
About 90% of the Port of NY/NJ volumes go through NJ. You get to have Staten Island and Red Hook (Brooklyn), us Jerseyans get to keep the ports in Newark, Elizabeth and Bayonne.
You, you say that like it’s a bad thing. I’m confused!?!
Take the southern tier y’all can have it. Headwaters region of our mighty rivers holds upper hand.
Are there still gold bars in Leavenworth? No matter 
Well trade say Wisconsin for Kansas. Grain and Gold 
Depending on circumstances / your aims, you could give up Texas and take Washington instead, though the oil in Texas would be quite tempting. The border with Canada might prove useful.
On the East Coast, I’d go with Virginia, Maryland, Delaware, New Jersey and New York. Significant population centers and lots of ports on the Atlantic, as well as a border with Canada.
Can you have one foot in each of the two states at the same time? Close enough for me! Colorado and Arizona might feel left out of the party though. And it would be difficult to move goods and vehicles between NM and UT without touching one of the others - so I wouldn’t recommend choosing that configuration.
If you go with the California-Texas region it might be better to have Oregon or Colorado as the fifth state instead of Louisiana. LA has some geographical strengths but the old time conservatism which is dominant there is not helpful to a new nation wishing to move forward.
Let’s make this interesting
Ok then, California should count as 3 states, since it’s the fifth largest economy in the world and maybe someday the fourth. So no merging with Texas.
Also, you get Rhode Island, Connecticut, New Jersey, Delaware, Oklahoma, North Dakota, Montana, and Wyoming free with any adjoining state. Mississippi and Alabama are considered a single state, so Texas and Florida have an easier land bridge.
Unchanged: attackers get 3 dice, defenders get 2 but win all ties.
Fine. Southwest Corner it is. California, Oregon and Arizona. Washington would be nice and a hold on the entire coast, but I would always be worried about my water supply and the Colorado R. I’d also annex (by force if necessary) Clark County, NV. That smooths out my borders a bit and gives me control of Lake Mead.
Hmm, under the new rules I might switch to the Great Lakes region, OH-IN-IL-MI-WI. Fresh water, warming climate, lots of agriculture yet still contains seven major cities and a host of smaller ones. Manageable population around 45 million.
I regret having to leave off Minnesota and might be talked into swapping it in for Ohio.
I’d take CA, NY, MI, IL, and OR. Red states need not apply.
The OP specified contiguous states.
In that event, I’d go with MI, IL, OH, WI, and MN. Had to pick OH over IN, being a bit less red.