If the point of Keynesian spending is to inject money into the economy to make up for diminished private demand, then an equally valid Keynesian stimulus would be to reduce taxes and leave the money in the private economy in the first place.
Which, in fact, Keynesians actually recommend: Galbraith, John K, The Great Crash 1929. And as that Evil Republican (!?) John Kennedy actually did in the early ’60s, that Evil Republican Ronald Reagan did again in the ’80s, and that Evil Republican George Bush the Younger did yet again in the early 2000s.
Spend more, tax less—either one produces the deficit spending that is actually what Keynes thought appropriate. Except that taxing less—eliminating the government as (inefficient) middleman in the deficit spending—produces the more efficient stimulus, to the extent that government stimulus can have any beneficial effect at all. And spending more is how politicians buy votes.