Sounds like the carbs are flooding. I do not know the SRX but I think it has a vacuum tap on the tank - is it on prime (no valve) or is it on run and the diaphragm not sealing? Is the float valve in the carb closing off - may be some dirt on it, ditto are the floats floating and closing off at the right point? Is this with the choke on or off - if on, try turning it off - if off sounds like the float bowl overflowing. Could try draining the float bowl - is their a drain screw and quickly trying to start the bike as the bowl refills - may give a clue before dismantling the carb.
Maybe I should leave this to someone who knows SRX's
R