No. While this is no means a guarantee, most donations on GoFundMe are simply considered to be "personal gifts" which are not taxed as income in the US.
Additionally, only donations made to a legally registered non-profit or charity may be considered eligible for donors to claim as a tax deduction. In other words the tax law is very clear that donations made to an individual are never tax deductible.
Gifts would have to be substantial from one person and for one person before any gift tax return would be required by the donor.