I'm not sure exactly how much per day it costs to run the White House but I've read online before that it cost around $1.4 billion dollars per year to run the White House.
So that would be around $500,000.00 per day or maybe more to run the White House Per day which includes the Utilities and everything else.
It's very expensive to run the White House but it all comes out of our Tax Payers Pockets so it's no problem for them.