JFTR, under the existing rules, Rand Paul does NOT have to choose between running for President and running to keep his Senate seat.
In Kentucky, he can only be on the ballot for one office at a time. He can be on Presidential primary and caucus ballots in all of the other states and territories while being only on the primary ballot for Senate in Kentucky. So he could run for Senate in Kentucky while running for President everywhere else.
In a close GOP nomination race, this might make a difference, but given that the norm is for candidates to either win the nomination by a comfortable margin, or lose, the fate of his Presidential campaign is not likely to hinge on whether he’s eligible for the votes of the Kentucky delegation. (The author of the Mother Jones piece disagrees on this point, saying “to have a realistic shot at the presidential nomination, he will have to win Kentucky.” I’m not seeing it.)
The other thing is, as the MoJo piece also mentions, the Kentucky primary is currently scheduled for May 17. I don’t know how far in advance Rand would have to choose, but my dim recollection is that such deadlines are usually 30-60 days in advance of the primary. By March 15, 25 states will have already had their GOP primaries or caucuses, including several big states like Texas, Florida, Illinois, Ohio, and Michigan.
If he’s still legitimately in the running at that point, he could (and should, IMHO) drop out of the Senate race to continue to pursue the Presidential nomination, so that other Kentucky Republicans have time to campaign for the nomination. (Also, if he’s still got a genuine shot at the nomination after March 15, it’s a safe bet that his campaign’s money problems will ease off considerably.)
If he’s not really in the running anymore by then, but still wants to stay on the campaign trail in the Presidential race, then it doesn’t really matter if he doesn’t pick up Kentucky’s delegates for the nomination: he can stay on the ballot for Senate in Kentucky, while not being on the Kentucky Presidential primary ballot, and continue to run for President for show.
ISTM that it’s only a dilemma if Rand still has a genuine shot at the nomination after March 15 (but is far from a lock), yet still wants the fail-safe of his Senate seat as he continues to run for President. If he’s in that position on the morning of March 16, he should simply man up and decide which way he’s going to go.