This is a phrase that you use when someone isn't very selective. In other words, if someone says "yes" to everything, even though it's a bad idea, use this phrase:
She'll sleep with any guy that comes along.
You're highly qualified, so it's not like you have to take every job offer that comes along.
In the example above, the speaker says that they can't take in every stray "that comes along". She means that they have to be more selective in deciding which animals to keep.