If Democrats push for Atchison to remain President till 1856's election (3/4/57 actually) then the Whigs could have another card up their sleeve.
It ws said that Atchison could simply act as president while retaining his Senate seat; not as bad witht he Senate and House out of session, but the Whigs may contendthat Atchison must be replaced. So, it's not certain that Atchsion would face an easy election contest in 1854. they could get behidn Benton in Missouri to unseat him.
Yet if he resigns the Senate, does he cease to be President Pro Tem and thus cease to be Acting President?
He likely gets around this by the Democrats pushing through an addendum to the 1792 succession act which clarifies what Tyler and Fillmore had already done through their actions - the person is now President and not just Acting, and therefore he must resign his Senate seat. Yeah, he might lose the seat to Benton because of this, but he would gladly do that to gaint he White House.
I see im going after Cuba - after reading the discussion I think he asks someone like Buchanan (Sec'y of State under Polk) to negotiate OTL's Gadsden Purchase but more land, and then try to purchase Cuba, while the debate goes on, not appoint an actual Sec'y of State, but then once the 1792 Act is amended appoint Buchanan as actual Secretary of State.
So, in 1856, the whigs will have complained but been unable to do anything, and by this point they'll be a dead party and likely evolving into the REpublicans, anyway. Even without Bleeding Kansas, they would be able to claim Atchison was usurping the post and that the Senate and hosue had "made up the rules on the fly." I can see it still becoming a totally alti-slavery and anti-expansion party.
The problem is the Stephen Douglas might bring up the idea of the Kansas-Nebraska Act anyway, because there were a number of popular sovereignty Senators and others in Washington, and Spain might not be willing to sell Cuba to the U.S.. If Atchison shoots the idea down. he would start to lose face int he minds of Southern Democrats, and Douglas might try to challenge him in 1856. However, if h4e supports it, he's going to upset a lot more Whigs and Northern Democrats who don't support popular sovereignty.
So, I think the question will be, who dos he want as his opponent in 1856?