Though I doubt that Crockett would be able to undo all of the Indian Removal Act, the more I look at it the more I think that Crockett might actually be able to pull off an upset in the 1832 election...
From what I've been reading Jackson's dominance of the South in OTL's election was more due to the fact that Henry Clay was incredibly unpopular there rather than his own popularity. Unlike Clay who attracted no support from the south in his presidential bid, Crockett would succeed where Clay failed. He might even attract the support of John Floyd and the other nullifiers and perhaps pick up some states in the south. However his opposition to Indian Removal might cancel out his support for state's rights as would his party positions. Most definitely, the Whig Campaign of lambasting Jackson as "King Andrew" would be much more effective. Add to this perhaps more disunity over a VP pick and there might just be enough to give Crockett the win. Who knows maybe Crockett manages to co-opt the Anti-Masonic Party, Nullifiers, and Discontented Democrats into an Anti-Jacksonian Alliance?
Who would he pick as his VP? If he picks John Floyd he'd attract nullifier votes in the south but risks losing his base in the north. If he picks Clay he's screwed, and if he picks a New Englander he runs the risk of not picking up any southern votes. Any Ideas?
Assuming he wins he'd be the youngest President ever elected at 45. Given Henry Clay's power within the party I'd expect that he'd be made Secretary of State if he's not given the VP.
Regarding Indian Removal, I think Crockett would try to secure a better deal for the natives, avoiding some, but not all, of the Trail of Tears. The Second Seminole War is almost certainly avoided and I'd expect new treaties to be signed with the Native Americans in order to secure their current lands.
Fast forward a bit and I could see Crockett's star begin to fade in the the south. Perhaps he looks towards Texas as an attempt to curry favour with the south and intervenes in the Texan Revolution? The War ends up straddling the Election of 1836 in which Crockett in all likelihood defeats Jackson and wins a second term.