Typically minimum CC payments are roughly 2-3% of your total debt. So on $20k that would be about $600/month. You can totally do that on $40k if you budget right.
You're right, you cannot declare economic hardship on your CC debt (well not for more than 1 month at least), but consider that even if you declare that on your student loan debt, you are still accruing interest. So basically even if you could roll it all into a student loan consolidation, you would be paying say 2-3% on that $20k of CC debt vs the $600/month you could be paying down on it if you BT it to a 0% card.
What I would do, if you find that you are really having problems paying, is:
1) cut up those d@mn cards and never use them again
2) put your loans on forbearance or deferment (whichever better suits your needs). There are special deferments for drs while doing their residencies. I just read this on the Sallie Mae website.
3) pay as much as you can towards your CCs until you can manage both a CC payment AND a student loan payment. Ideally you could get rid of that CC debt before having to start repayment on the student loans. If you could pay $600 a month with 0% interest, you would have $20k paid of in 34 months.
The bottom line is that you have to suffer the consequences for having used the CC (this isn't a judgement, since I am jsut as guilty of having used mine, it's just the facts) which means paying them back when the banks want their money. Whatever you do, DO NOT miss your payments on them bc that will trash your credit report/score and you could have trouble consolidating your student loans down the line. Do whatever you have to do to get them paid off as soon as humanly possible then worry about the student loans (although don't just ignore them... you need to delay the payments in a legal manner since missing those payments will trash your score as much as missing the CC payments).
If you find that you really cannot make it, then you could try credit counseling but this will hurt your credit score/report for the next 7-10 years and honestly, I don't think it's worth it if you are in an ok position right now (meaning you have not been late or missed payments yet). Same goes with bankruptcy. But I wouldn't go that route until I found that I could not feed myself basically.