I know that NASA has sent many, but due to the harse surface conditions of Venus, I have yet to either hear or read about any of them surviving. I believe that the USSR sent many as well , and at least one of them managed to last for about an hour or so, but no longer. Has the United States ever sent one that actually landed on the surface and survived for any given length of time?
Yes, sort of. The Pioneer Venus spacecraft in the 70s carried four small probes released into the atmosphere, one survived on the surface for about an hour. This was a bonus scince they were not designed to do that.
Right. Venera 9 and a few other Soviet-era probes actually landed, and so did that probe from Pioneer-Venus (it helps that the supefying density of the Venusian atmosphere means a much slower terminal velocity). But besides those probes, NASA never actually sent a lander.