I'm currently playing a game where US (ai-controlled) selected Reject Manifest Destiny, and actually... almost nothing has changed. The US still stretches from sea to sea. The Cherokee events appear to have been slept, it doesn't have the South - due to my intervention, the CSA won the war - and Russia refused to sell Alaska, but all other parts of the mainland US are blue. In fact, it's even bigger, since it went with 54'40'' in the Oregon Treaty (UK backed down), conquered a good bit of Mexican land, and in various wars with UK annexed New Brunswick and Nova Scotia!
A few weird things did happen. Guadalupe Hidalgo seems to have been slept (at least, the Mexican event; the US one did trigger, but obviously did nothing), so that war ended normally (with New Mexico and a good bit of northern Mexico becoming American). The Bear Flag Revolt broke out, causing California to form, but soon after the USA attacked CA and annexed them in a series of two wars. And lastly, Deseret was conquered by the US in war, rather than joining peacefully.
(On a side note, I've never seen Deseret join the US peacefully in several games of VIP. Does anyone else have this problem? Is the event chain broken somewhere?)
I must say I found this rather unsatisfying. I'd kind of hoped that a US without Manifest Destiny would limit itself to the East Coast. But no such luck - they kept cores on the upper Midwest and the Pacific Northwest, the Indian events fired as normal (at least, the Aztec, Sioux, and Nez Perce ones), and the normal US formed. Is this WAD? Wouldn't a US that refused Manifest Destiny also refuse the Pacific Northwest, ceding Columbia to the UK without the need for an Oregon Treaty? If there were no American sights on the southwest, wouldn't the Bear Flag revolt never have happened, and Deseret (assuming the Mormons still did move West) feel much less pressure to join the US? Wouldn't Mexico have kept its hold over the Aztecs?