put a streight round bar in a tool holder and put it in the spindle. Then put a .0001 indicator on the round bar and push the bar with your hand. If you can deflect the spindle more then a tenth or two with your hand you have a bearing problem. But not very likely. My next guess is there is something going on with the tool retention system.
That could be very dangerous so call the Haas doctor right away! Or you could be lucky and it's just a sheet metal issue or harmonics.
Be carefull what you wish for, you might get it.