No. Gifts are not taxed to the recipient, regardless of amount or whether they are from people in or outside the United States. If you make gifts, you need to check on whether you must pay any gift tax (not income tax) and/or whether you have to file a gift tax return, Form 709.
Eligible taxpayers may claim a tax credit for 10%, 20%, or 50% of up to $2,000 of retirement plan contributions.