Borrower funds used for the down payment, closing costs, and reserves must be "seasoned" for two months before they can be used to qualify for a mortgage. This means the borrower must be able to provide proof that the money has been in their account for two months. Cash on hand is not an acceptable source of funds for most loans. If someone is going to use cash on hand to qualify, they need to put the money in the bank as soon as possible.
If a borrower has a joint account with someone who is not a borrower, the money in that account can be counted, provided the person who is not the borrower states that the borrower has use of all the money in the account. The money must still be seasoned for two months to count it.
A borrower can also receive a gift from a relative for certain types of loans (most notably FHA loans). In the case of a gift, the money does not have to be seasoned. It must be deposited into the borrower's account before the loan can get a final approval, but it does not have to be in the account for a full two months. One day is fine.