There have been numerous veeps die in office, and numerous presidents that served without a veep. 
These served without veeps for an extended period of time:
Tyler
Fillmore
A. Johnson
Arthur
T. Roosevelt during first term
Coolidge during first term
Truman during first term
LBJ during first term

So, it is not without precedent having a vacant veep postition.

"The best way to teach your kids about taxes is by eating 30 percent of their ice cream."  Bill Murray