George .W. Bush was appointed as a Republican President where he raised taxes as a way to reduce the national budget deficit. Bush declined many times although was making no improvement with a Senate and House that was controlled by Democrats.
That's not the President's job. Congress has the "power of the purse." President Nixon tried to not spend what he was budgeted, and was subsequently sued by Congress, forcing him to spend the money. President Reagan made a deal with Congress: for every dollar of tax increase, there would be two dollars of deficit reduction. Congress had no intention of honoring the agreement.