A failed Gadsden Purchase in 1853 could very well have knock on effects of garnering more support from the South for Walker's expedition to Sonora-Baja. There was a lot of unrest in northern Mexico during Santa Anna's latter reign. Furthermore there were several cross border incidents in the latter 1850s that a pro-South Buchanan may have exploited to create a new casus belli. It's not hard to imagine northern Democrats and remnant Whigs going along with what is perceived as a sop to the South in return for a free Kansas.
Thus, no Gadsden could easily become an even larger "purchase" just few years later.
Even better have the Second Mexican-American War begin in 1860 due to the Cortina Troubles. The North, angry that once again the nation is embroiled in a war to expand slavery, still elects Lincoln. (Possibly even Seward if they're ticked enough.). And you get a three way war where Northern and Southern troops have to choose sides while already deployed in the field.
Benjamin
The original plan for the purchase was in fact much larger, it included more of Sonora and all of Baja California. Santa Ana was all for it because he wanted as much cash as possible to build a larger military. To paraphrase a saying- he was willing to cut off his nose in order to strengthen his hand. Doesn't make sense to us today that he'd sell of a big chunk of land for cash to strengthen his military against US incursions, the very people he was selling the land to. But in his perspective he felt he was losing the land regardless, and better to lose it in his terms and have a better shot in the future. It was the US that limited what was bought.
Las Vegas almost certainly is going to Nevada. Callville is the head of navigation on the Colorado (as far upstream as steam boats can reach) and Nevada being a state and the thinking of the time that states deserved "sea access" pretty much assured that the triangle we associate now with Las Vegas would go to Nevada. At the time it was all about Callville and the Colorado River.
After the Mexican-American War New Mexico was proposed as an immediate state, at this moment the Texas border had not been determined and California similarly was going for immediate statehood and working on its borders, and you had Deseret as well. New Mexico proposed to be roughly the eastern half of Arizona and much of southern Colorado, along with Oklahoma panhandle and Texas panhandle. As with all big state proposals (such as California's original proposal to be Pacific to Rio Grande; and Texas proposal of Rio Grande; and Deseret of Los Angeles to Denver) this wasn't approved despite the President's agreement and pushing for it. A New Mexico with Arizona in my opinion leads to the northern border shifted south to be in line with the Missouri Compromise line (Texas' northern border instead of the current border in line with Oklahoma's northern border), this along with Nevada getting Las Vegas makes a greater New Mexico more in line in geographic size with other states. This small strip (same proportion as Oklahoma's panhandle) gives some extra land to Colorado and Utah making that state and future state bigger just enough and greater New Mexico just small enough as to not worry people as California and Texas did. Colorado's extra-legal predecessor the "state" of Jefferson in fact did claim that strip. The problem for Utah is that Congress at this time hated Mormons and hated Utah; giving them extra strip will lead to Nevada being pushed east a bit more probably, Nevada had been given several moves east to take Utah land three times already just as punishment to Utah and to make Nevada larger.
