Short answer is yes.
Any policy that deal with money is possible to implement by the government institution.
Example : Once upon a time, the USA government say it is impossible to track and trace illicit money run in the bank. September 11 happens and everything change.
As for Sanders example, it is possible to implement a system similar to Australia Higher Education Support Bill. However, since education loan is a trillion dollar business (direct loans and derivative), finance companies are definitely going to spend hundred millions in lobbying and media propaganda to demonize such idea.
Many will argue that this against "free market", but in fact, without government bail out finance company and corporate during financial crisis, a lot of corporate America will ceased to exist today.
In fact, if 20% of USA population default their student loan, it will caused a finance meltdown similar to sub-prime meltdown in year 2008.
@Andrew Grimm point out that the loan is guaranteed by USA government. In fact, a guaranteed loan means little to shield banks from massive liquidity shortage. It all depends on the scale of the student loan default, i.e. the subprime does't meltdown in one day, it is the snowballing default that crack the camel back.
In fact, the guaranteed loan policy also give us another conclusion : private bankers that provide student-loans is simply a rent-seeker.