True- deficits and debt are different things, though deficits cause debt. And continued deficits can create an unpayable debt, which is the directions we are heading. Both parties cause this for their own political means whether it be guns (historically R) or butter (historically D).
Debt payments have not stopped under any administration I can think of in recent memory as that would be absolutely terrible for our fiscal policy. (If we fail to pay our debt, fewer players will buy bonds in the future (i.e. lend us money)). I can't see any administration supporting this as a strategy as said administration would be significantly constrained in running a deficit within a fiscal year.
It's probably a political tactic and not a long-term strategy.