Personally I think its good to have some savings cushion. You can't eat/pay rent/fix your car with paid off loans but you can with emergency funds. I would recommend setting up a solid emergency fund (at least 2 months of expenses) then tackling the debt. A lot of money gurus recommend an emergency fund of 3-6 months expenses, but that can take awhile and if you have high interest rates on your loans might not make sense. Dave Ramsey recommends just $1000 until you get your debts down. But it all depends on what you will feel comfortable with based on how secure your employment, what your back up plan and how much you can save each month.

Personally, I saved a year of expenses and made sure to max my IRA and get my 401K match before hitting my student loan debt heavily. But that's because I felt my job was unstable and wanted to make sure I could survive if new work wasn't forthcoming. If I was more secure in my job at the time, I still would have contributed to retirement savings but built up less of an emergency fund.