Here's my advice, if you can't pick up a song instantly, don't get discouraged. Just because you are a musician, that doesn't mean you can play any and every song known to man at the drop of a dime. And don't let other people make you feel bad because you can't. Picking up a soloist is NOT essential, it is a learned experience.
Another thing is the term "popular song" doesn't mean diddly squat to me. Just because it seems like everyone and they momma sing it, that doesn't make it a must know for every musician. Some people need to to either bring their own musicians, or have a CD ready for those moments.
When I don't know a song, the first thing I do is DON'T PLAY. There's nothing worse than a musician fumbling through a song. What I like to do is see if I can form a chord progression that goes with the song. It may not be correct, but it will work for the time. If none of my ideas seem to fit, then I just let them sing acapella.
If you can find the 1 of the song, then your in business. And usually before the 1 is a 5, and before that possibly a 2. So, u got three chords right there w/out really even thinking. After the one, follow their voice and go through different progressions in your head. Once u got ur pattern, get the key and go for it.
Chording by melody alone is complicated. Plus, these days the bass notes people use to go with the melody sometimes doesn't fit together at all. Unless you know the song man, it's really hit or miss. Sometimes you hit, and sometimes u bomb and just need to not play at all. Non-musicians will never really understand this, so when they start talking about you, just let roll off your back and keep going. Like Jesus said on the cross, "Forgive them, for they know not what they do."