Once it really takes off, I think you'll be over 500k per day, based on the past relationship between the UK and US. The US is so big it takes a bit longer. But typically, you end up with about the same number of cases per wave and 15-20% more deaths (more antivaxxers), on a per capita basis.
Our pandemics have been roughly comparable although we usually seem to be a few weeks ahead, as you say.