This will definitely vary by level; minion damage goes up by less than 1 point per level, while PC hit points go up at least 4 points per level, so PCs will become sturdier in relation to the amount of damage minions can do.
Hm. Let's work out a light version of the math. For the sake of argument, let's say your PCs kill about 1 minion apiece per round. Some will manage more, some will manage less -- it's a working average. Minions should hit PCs about half the time. At first level, minions are doing 4 points of damage, which is maybe a sixth of a typical PCs hit points at that level.
So 20 minions will do 10 chunks of damage on the first round. Spread it evenly; you've got all the PCs 1/3rd of the way down. 5 minions are removed by the brave PCs, leaving us with 15. On the second round, 7 of them do damage, and all the PCs are bloodied. Then we're down to 10 minions, 5 of whom do damage; then 5, 3 of whom do damage; then none. Total chunks of damage is 25, which leaves the PCs seriously hurt but not down.
That's kind of a poor approximation since it didn't figure healing, and it assumes the minions are too dumb to focus fire, but it might work OK for a rule of thumb. What I've done in practice is stage minions (or other monsters) in waves. When the PCs are bloodied, you can hint that the flow is slackening. When they're close to down, you can throw in one more wave and call it done. If you keep a straight face your players won't ever know.
On the other hand, that might violate the game contract -- I tend to run for effect more than simulating a world, and some people dislike that, which is cool. To each their own! So I'd think about social issues before using that piece of sleight of hand. Choosing to focus or not focus fire might be a more acceptable way to go about it; those minions, as noted, will be much more dangerous if they all attack the healer on the first round.