Man, I was thinking about maximum speed rather than minimum speed 
Quick question.... is 3.14 m/s for a bird practical?
3.14m/s=3.14*1000/3600=11.30km/h
The slowest moving bird apparanetly has been clocked at 5 mph = 5*1.61= 8.05km/h http://wiki.answers.com/Q/What_is_the_slowest_bird_in_the_world, http://en.wikipedia.org/wiki/American_woodcock
So it can happen, but not for all birds.
Remember that lift increases with the sqaure of velocity do at low speeds, only a small amount of lift can be generated to counter-act the weight force, so only smaller/lighter birds would be able to fly at this speed. But it is possible. Lets call this "plausible" (out of confirmed, plausible and busted).
Also, there's nothing to say that the bird didn't start flying, then slow down to such a speed that lift exactly equalled the force of gravity pulling it to the ground, leaving it flying at the slowest speed it could possibly go at. Assuming it was at least a few meters off the ground it could probably do this quite safely.
Likewise, sometimes birds take advantage of those rising columns of hot air that hang gliders use in order to fly. I would imagine a bird could take advantage of these to fly quite slowly (they appear to hardly move when they are flying in them sometimes)
It's probably going to have a hard time finding that exact speed since if it is flapping it's wings, the forces are not constant but irregular and cyclic, if its gliding, it may find this speed for an instant but it will still encounter some air resistance, so it will slow down past this speed.
Yeh the hot columns of air would work, kinda similar to if the bird had a head wind of the exact speed to keep it in the air, then try to get the forces in equilibrium in a gliding position (now that I think about it, thats probably what you meant above). It's relativer airspeed would be different to it's actual airspeed, and so it's airspeed compared to the ground could be 0 m/s but compared to the air, 3.141592653589.... m/s.
EDIT: Geez we really are bored, we are talking about the aerodynamics of birds.