1000s of people will likely die due to the primary and secondary effects of the lockdown (suicides, delayed health care, etc.). There's also no guarantee that "locking down" will actually prevent any deaths - it may just be delaying them until the point where things start to open back up (because I think we can all agree that does have to happen at some point someday). Everyone is hoping for treatment or a vaccine or really good testing/tracing to make a difference, but I'm not sure any of those things are guaranteed. We may just be delaying the inevitable.
All decisions at this point have significant downsides. There is no clearly correct answer. Politicians are trying to balance those concerns, and they're trying to do so with extremely limited data and awful models (due to the bad data - GIGO). I don't honestly think anyone knows what will really happen with either the virus OR the economy. It's clear they're just guessing and that's really terrifying.