If my closing funds are short by a small amount, can the deal still close that day?

Not automatically, even if the shortfall seems trivial compared to the overall purchase price. Lawyers work from precise trust accounting requirements and a detailed statement of adjustments, so a shortfall, however small, generally needs to be identified and resolved rather than simply overlooked, since releasing an incomplete amount toward closing can create accounting and professional problems for the lawyer involved.

In practice, a small shortfall is often the easiest kind of closing-day problem to fix: your lawyer will usually flag it as soon as it is discovered and ask you to send the difference immediately, whether by an additional bank draft, a quick transfer, or another accepted method. Whether this can still happen before closing depends on how quickly you can get the money to your lawyer and how much flexibility the seller's side has that day. If the missing amount cannot be provided in time, the closing may need to be delayed by a short period, similar to any other funding shortfall, even though the amount involved is small. Confirming your final closing costs with your lawyer a few days ahead avoids this entirely.