AAMC website has a really nice loan calculator set-up
https://services.aamc.org/30/first/home/organizer.
For 280k in unsubsidized Stafford loans taken out during the first year, a 3 year residency, and the lowest average salary (135k, peds. btw) using forbearance, and paid over 10 yrs, you will have monthly payments of $4,800.
I used this website to calculate out tax information
http://www.yourmoneypage.com/withhold/il2.php
Assuming 135k annually gives you 91k after state and federal taxes (this is is Illinois with no withholding, so definitely a low ball estimate) which equates to $7580 per month.
Minus the cost of repaying loans leaves you with ~$2780 per month. Is $2780/month glamorous, not really, but it's still enough to live off of. Also, these numbers assume worst case scenario across the board; most likely annual pay will be higher and you wont be making your starting salary 5-10 years post residency. This is also assuming you want to pay off your loans straight away. There are several other options for repayment which will leave you with more take home pay, but a longer pay period and overall greater repayment.
So in answer to your question, yes it's reasonable to repay all of your loans. You might have to live within a tight budget for a few years, but you'll come out with a significantly above average salary (nationally) in one of the most stable career fields.
*I took a lot of liberties with these calculations, and a realistic loan plan would not look exactly like this. However, I think this still paints a somewhat realistic picture of the effect loan repayments will have on post graduation quality of life.