For inflation to happen in the wake of the stimulus, the spending would have to lead to too much money chasing not enough goods. Blyth gives some pretty good reasons to be skeptical that this will happen.
Start with the wealthy: they don't spend much, relative to their income. Their consumption needs are already met (that's what it means to be rich). You can only own so many Sub-Zero fridges, and even after you fill them with kobe beef and Veuve Cliquot, you're still rich.
What rich people do with extra money is speculate. That's why top-level giveaways generate socially useless, destructive asset bubbles. Remember, these aren't inflation, which is good, because everyone agrees that inflation is hard to stop once it gets going.
They're speculative bubbles. We have a much better idea of how to prevent bubbles: transaction taxes, hikes to the capital gains tax, and high marginal tax rates at the top bracket.