Kind of like mask-wearing. The government was running around telling us it didn't work, while desperately trying to make sure hospital workers had enough masks. Meanwhile, Asian countries where mask wearing is considered good public hygiene when ill or during an outbreak all adopted it en masse and mitigated their COVID-19 epidemics much faster. This has all deservedly cost the US government, our anti-science President, the CDC and other agencies vast amounts of credibility.
As another poster implied, the President is so bad at his job of reassuring the nation and communicating complex information in a convincing but straightforward and believable manner that he would be much better off shutting the fuck up and saying "I am going to let the experts address this". What some of these Trump supporters call "Trump derangement syndrome" is just rational, well educated people reacting to an imbecile in the office who couldn't reason or explain his way out of a paper bag. Trump has some good advisors around, and some of them are surely feeding him good information from time to time, so he isn't always wrong (though he frequently is), but he ALWAYS sounds like a moron when he opens up his mouth.
It seems likely to me that HCQ is somewhat effective against SARS-CoV-2. I had what I believe was COVID-19 in early March (no tests available, fuck you California and your horrible lack of preparedness, so until I can get an antibody test I won't know for sure) and I megadosed on zinc lozenges and used benedryl and Albuterol to manage reactive airway inflammation and shortness of breath. I came through it fine, but it was scary and unlike any virus I have had in the past. I would gladly have added HCQ into the mix, but my doctor seemed to think I was doing fine and it wasn't so widely discussed then. I am a scientist, but recognize that in many scientific fields we have to make timely educated decisions based on less than perfect evidence.