Why not, the USA had already grabbed the first half.
With full Southern support at least from slave owners.
You undersell the situation.
Texas was settled by Southerners, founded by Southerners, and annexed because of Southern interests. A Southern president deliberately provoked a war over the disputed border for Southern interests and acquired Mexican territory primarily for Southern interests.
It's grossly disingenuous to pretend that because no entity called the CSA existed prior to 1861 that nothing the USA did pre-1861 had anything to do with the South. The federal government did not ignore antebellum Southern interests. It waged wars to support Southern interests!