I would think that a lot of brokers would put the restriction suggested in @homer150mw in place or something more restrictive, so that's the first line of answer.
If you did get assigned on your short option, then (I think) the T+3 settlement rules would matter for you. Basically you have 3 days to deliver. You'll get a note from your broker demanding that you provide the stock and probably threatening to liquidate assets in your account to cover their costs if you don't comply. If you still have the long-leg of the calendar spread then you can obtain the stock by exercising your long call, or, if you have sufficient funds available, you can just buy the stock and keep your long call.
(If you're planning to exercise the long call to cover the position, then you need to check with your broker to see how quickly the stock so-obtained will get credited to your account since it also has some settlement timeline. It's possible that you may not be able to get the stock quickly enough, especially if you act on day 3.)
Note that this is why you must buy the call with the far date. It is your "insurance" against a big move against you and getting assigned on your short call at a price that you cannot cover.
With the IRA, you have some additional concerns over regular cash account - Namely you cannot freely contribute new cash any time that you want. That means that you have to have some coherent strategy in place here that ensures you can cover your obligations no matter what scenario unfolds. Usually brokers put additional restrictions on trades within IRAs just for this reason.
Finally, in the cash account and assuming that you are assigned on your short call, you could potentially could get hit with a good faith, cash liquidation, or free riding violation when your short call is assigned, depending on how you deliver the stock and other things that you're doing in the same account. There are other questions on that on this site and lots of information online. The rules aren't super-simple, so I won't try to reproduce them here. Some related questions to those rules:
An external reference also on potential violations in a cash account: