In the US, the recipient of a gift does not pay gift tax. You must file form 3520 to report the gift, the deadline is the same as the tax deadline; for a gift received in 2020, the form is due April 15, 2021. You file it separately from your tax return. Turbotax does not prepare this form, you will need to do it yourself.
Naturally, if you hold the gift in an interest-paying account until the house closing, you will owe income tax on the interest.
