In practice, this will be a Mexico-wank. If they fight for independence, they won't be called New Spain. Though you can conceivably come up with alternate names, capitals, etc., you're basically looking at a more successful Mexico, with its capital at Mexico City.
I'm not up on Mexican history like I should be, but I do know that it has always been relatively unstable, in part because of a continuous conflict between the old Spanish-Mexican elites and more democratic-republican forces. Before they could sort it all out, the US came along and took their entire northern frontier.
So, consolidate Mexico as either a stable Republic or a stable Empire, and butterfly away the conflict with the United States. Balkanized United States (in which case Virginia takes up the role of the OTL United States, at least as far as Mexico is concerned), a Henry Clay victory in 1844 and/or generally less expansionistic events, a US that is for whatever reason stopped at the Mississippi--the Louisiana purchase is blocked by aggressive British action, for instance, all prevent the juggernaut from taking Mexico. Mexico can also win the OTL Mexican-American war if they manage to come up with some of the things that IOTL let the United States win despite fighting with inferior numbers on enemy turf: a superb officer corps, and superior communications and logistical infrastructure.
From there, we have a nation that stretches from the Yucatan to California. Perhaps it keeps some or all of Central America, as outright territory or satellites as well--I don't know. If it can keep the loyalty of the anglo settlers who will be heading westward, it has even more going for it. It can build the TTL equivalent of the Panama Canal on its own soil. When the great European conflicts of the 20th century emerge, it can stay isolated or join them and, as the United States did, take the torch of Western Civilization from the old world into the new.