How Much Should I Practice This Chord?

Normally I can't specifically answer the "how long will it take?" kind of questions, but I suppose this isn't exactly one of those.

This student is doing it wrong.

•  Let's say you've got to play a hypothetical song, and it's a slow one: a tempo of 60 beats per minute.
•  Let's also say that you've got to play a chord every quarter note.  So in other words, 60 chords a minute.  A chord every second.
•  Let's say the average length of a "song" is AT LEAST 3 minutes long.

 You've got to be able to play a chord 180 times in a row, at a pace of 1 a second.  Sure, most songs aren't based on 1 chord over and over, but you're still squeezing, releasing that many times at least.

 This is presuming a very slow tempo, mind you.  So conservatively, in reality - you need to be able to do twice that, in order to have a little bit of lee way in your ability to be able to say "yes, I can play this song".

 360 times, at a pace of once a second would be a nice target.

 "Man, Chip, that's a lot!"

 That's only 3 minutes.  99.9% of the people reading this won't bother to do this I realize, but I'm just throwing that out there: you NEED to be able to do this, AT LEAST.

 Maybe you press/strum/release a chord 50 times.  That's half what's really baseline.  A "nice workout" might be all of the open chords (G,C,D, Dm,A,Am, E, Em), 50 times every day.  Then there are the bar chord variations...

 The point being, to play an Average Pop Song you've got to get your musculature to the point where you're in that ball park figure.  So there you go: practice Said Chord 50x a day, at least, and aim for 180 as the goal.  360 to conquer it.  In reality, though - this is why you want to make playing along to recordings of songs your goal: you're "getting your exercise" by doing so, in a more interesting and entertaining way.