No, it's the giver who is subject to any gift tax, not the person who receives the gift. But a giver is allowed a lifetime exemption of (currently) $5.45 million without being subject to the tax.
If the gift is greater than $14,000 in a year, then he will have to file an IRS Form 709, US Gift Tax Return, for the year in which he makes the gift. The form doesn't trigger a tax; it simply documents the amount given in a particular year, for (eventual) calculation of the lifetime total.
So you won't pay tax on the gift, but remind your father-in-law that he will need to file the Form 709 for the year he actually makes the gift to you.
Here's some further reading on the gift tax: https://www.irs.gov/pub/irs-prior/p950--2006.pdf.
