Thanks for the input! This worked for me as well on our 2000 Camry. Instead of a metal object, I used a tie wrap to loosen the gunk up, and used a vacuum to clean the tube out from the bottom of the vehicle. Jacking up the vehicle was helpful and made it easy to get the hose of the shop vac to make a good seal around the drain port and really get the stuff out. Once the plug came out, a good deal of water came out as described earlier.
One other thought if this becomes a recurring problem, is they sell tablets for home AC units which go into the drain pan of the condenser and prevent the algae and buildup. I may grind up one of the tablets, mix with some water and inject it into the system from the bottom. But only if it clogs again.