John Oliver is horrible and dishonest and this piece is no different with his smears against Cruz and Mick Mulvaney. That said....
Debt and deficits can influence inflation, but ultimately monetary policy entirely determines inflation. Japan had deflation running the biggest deficits in world history because money was extremely tight.
The problem with government spending is it consumes resources and changes incentives and slows long term growth. But the current big spending probably isn't going to end in calamity. It is far more likely to end in a period of perpetually slow growth with high interest rates and high taxes.
