My experience has been that the hospital sets up the monthly payment amount (sometimes with varying plan options). You can't partially pay, and the payment amount is a simple ($total / plan term). Paying $1 isn't really an option.

The last medical bill my family had was something like $3500 and the longest term the hospital offered was 6 months, at $580/mo.

I'm sure they're not all the same, but I could certainly see an unexpected $580/mo being able to cripple a family living paycheck to paycheck.