Grayson's Restore the Tour Act, H.R. 3203, authorizes people to "make gifts to the United States Government to be used for the purpose of providing public tours of the White House."
That money would go into a special account used to fund White House tours.
The bill also allows the government to reject certain gifts if taking them is found to be "in the interest of the government."
The sequester has been overshadowed by the government shutdown, which has left thousands of nonessential government workers furloughed while Congress struggles to find an agreement for funding the entire government. House Republicans have said they will be in session on Saturday to pass more "mini" funding bills, a plan Democrats oppose.