The Manifest Destiny is still there, plus there's vengeance and competition with the Confederacy, many of whose leaders had rather delusional expansionist ideas themselves.
Hell, OTL saw the U.S. defeating the last of the Indian nations and conquering Hawaii and the Philippines AFTER the Union victory in the Civil War, which cost far more blood and treasure than an early enough CS victory.
I would rather like to know how the CSA plans on getting its hands on Baja and Sonora, as indicated on the map, and ask why the residents of those regions would be willing to accept a bunch of slaveholders as their leaders.