Total mortality based on civil records - this is commonly used as a check on medical reporting, as death is death, it does not depend on the ascribed cause of death, which can be subject to judgment calls and errors. In the US unfortunately this is not reported in a timely manner. It is at least a month behind, if not worse.
Anyway, as of the week of June 19 the US is still seeing excess overall deaths.
https://www.cdc.gov/nchs/nvss/vsrr/covid19/excess_deaths.htm
The curve will go up like you said. But it won't be like what we saw in the winter. So the increase will be small.