A history of mental health or a previous suicide attempt of your part is likely to stop you from being recruited into the US Army and consequently any branch of the military. The US Army place a high premium on a person's mental and physical status and you are most likely to be deemed unfit mentally to serve in and under the pressure and the strain that is involved in the US Army.
If they were before you turned 18 then no. If its something that is off recently then yes. My fiance tried to join and he was rejected due to being bi-polar and taking meds for that as well as depression meds and anxiety meds and anti-seizer meds.
Talk to a recruiter. Just about anything can be waived. You will have to be evaluated by a psychiatrist and verified mentally fit. Most important thing they want is honesty. Nobody can blackmail you if they already know about it! Just do it!