My father is a Swiss citizen residing in Switzerland where there is no gift tax. I am a US and Swiss dual citizen residing in the state of Illinois. My father is planning on giving me a gift consisting of money and stocks. Will I have to pay any kind of tax on this gift, state or federal and does it matter how large the sum is? How high is this tax? Thank you in advance for your answer.

If your father is not a U.S. citizen or resident, he does not file gift tax return or pay any gift tax in U.S.
Also the receiver of gift does not pay any gift tax.
Only requirement may be that of filing Form 3520. Your U.S. Tax Return: The U.S. Gift Tax

QUOTE," Will I have to pay any kind of tax on this gift, state or federal and does it matter how large the sum is? "---No!Anyone includin' you can bring unlimited amounts of money into the United States. As you can see, the US is the world's largest recipient of foreignmoney. But if the amount of money coming into the US from abroad via wire transfer( into your bank account) exceeds or equal to $10,000 , then your bank will report the amount to the IRS( US Treaury Dpt).That doesn't mean to pay any form of taxes on the money transferred into the US from overseas.Federal law requires that all banks report any cash deposits made in excess of $10,000 in the hopes of discouraging money laundering, rather than tax evasion. "wires" from abroad require the same information.
Also REMEMBER! You must file IRS Form 3520, Annual Return to Report Transactions with Foreign Trusts and Receipt of Certain Foreign Gifts,suppose, during the current tax year, you receive
Gifts or bequests valued at more than $100,000 from a nonresident alien individual abroad, in this case your father in Swiss.