or would a slew of state lawsuits prevent him from being on the ballot?

iirc, Colorado tried to keep him off the primary ballot, citing the insurrectionist clause of the 14th. SCOTUS said Colorado did not have authority to enforce Federal law.

So, basically, no, the states could not keep him off the ballot, by citing the provisions of an amendment to the Federal Constitution.

That's why I say Obama needs to say, publicly, now, that, if Trump runs in 28, he will too.

"If he runs, so will I. My top priority will be health insurance reform. The ACA was an imperfect stopgap, but it was the best we could get at the time. If elected, I will make it my mission to offer Medicare for everyone, financed by a VAT. No more complex subsidy schemes, that malignant actors can take away at their whim. No more employers forcing people to work, no matter how sick, to keep their insurance. Everyone gets health care insurance, because everyone buys things, hence, pays for their coverage. Don't be swayed by nonsense about "big gummit death panels". Private insurance companies that deny legitimate claims are the "death panels". Companies that force people to keep working, no matter how sick, to keep their insurance coverage, are the "death panels".

See? Messaging is easy, without the racism and religious extremism that the GOP has embraced.

Anecdote about employer provided health insurance. When I left the pump seal company, they brought in a young, fit, guy to replace me. A few years later, he developed cancer. The company required him to keep coming to work, or else they would take his health insurance away, and the medical bills would destroy him. Dave kept working, until the last few days before he died. The company didn't care about his welfare. They only cared about how much work they could extract from him. I find that monstrous, but that is how "health care" in Shinyland works.

Steve...Obama in 28