That is to say, the timing of the staggered increase was calculated so that the effects would not be known in time to be an issue for the 2018 elections. Which, frankly, if I was an incumbent worried that the tariffs might turn out bad for likely donors to my party's candidates, that's how I would time it.
I think the reason they left more stages was so they left more layers of uncertainty & had more in the bottle of pain to leverage later.
They could have waited an extra month from now and started with 25%, but by doing things in smaller stages they have better control of the narrative.
The lobbying flows pre-date the passage of anything significant. Even rumor of a scent of potential costs or regulations drive intense spending on the GET THE FACTS styled political (dis)information campaign front.
It is already over half-way through September. Elections are November 6th. That is a 50-day window.
If the tariffs came through full right away, much of them likely would not have been passed onto consumers that quickly. Retailers can show margin pressures so long as they show e-commerce growth (or spin the cause as being associated with heavy investment in growing ecommerce), but retailers can't show low margins, declining sales & limited ecommerce growth. Until Amazon's stock price seriously heads south (which might not happen anytime soon) retailers will do anything to hype their ecommerce growth, cross claim sales that touch a computer in any way as being ecommerce, lose money to keep volumes up at least until the holiday shopping season is through, etc.