I believe that there should be free options for college for all Americans. In the absence of that I would like to see many more student loan forgiveness possibilities. In the absence of that I would favor some pretty hefty tax credits/deductions for paying off student loans. But the absence of that too is what we have.
Student loans are tuition/fees/education expenses paid in the past, but are no longer deductible, so poorer students/families are penalized, while wealthy parents who can foot their children's bills get a tax break. The poorer individiuals get the benefit of the much smaller student loan interest deduction: only up to ~$2500, and not at all if AGI is >$75k. So M.D.'s with $125k in loans, but $150k in income get no breaks. (I think they can afford it, but that's another issue).
Since the first two just won't ever happen (as far as I can tell), the third issue is the only one with a chance to get real traction...
It is an incentive to pay off early. It allows lower income individuals to recoup tax breaks that the wealthy in this country get anyway. It would provide a pretty sizable stimulus to people most likely to spend extra money. In providing an incentive to pay off student loans it also could lower the default rate...particularly for higher income individuals like MD's. Since the US guarantees those returns (to private companies no less) then a lower default rate means some savings (no, not nearly offsetting, but some).
On the minus side, it would be pricey, and could encourage education expenses to accelerate (I would restrict to US backed/insured loans, which helps here). Better offsets, like by elimination or reduction of the mortgage interest tax deduction, are less likely than worse ones, like a increase in taxes on the wealthy, or simply none.