From this source:
“QUESTION: Taxing the Obamas
ANSWER:
President Obama is not taxed on the value of living in the White House under a section of the tax law that makes such value tax-free because the lodging is being provided for the convenience of his employer (the U.S. government). If his mother-in-law is his dependent, her lodging is also excluded under the same section of the law. If he lets her stay there for child-care purposes, but she’s not his dependent, I’d say she’s his house guest. And since presidents aren’t taxed on allowing guests to stay in the White House, I’d say he won’t owe tax on his mother-in-law’s use of the home.”
—Kevin McCormally, Editorial Director, Kiplinger Washington Editors