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.
For calendar year 2007, taxpayers covered by an HDHP may contribute up to the lesser of the annual deductible or $2,850 ($5,650 for family coverage).