First, let's define our terms. People certainly can default on their student loan debt now. To default on a debt is to stop paying it. Then the debt goes into collections. What you presumably want to know is what is the difficulty with easier discharge of student loan debt in bankruptcy. The current rate of discharge for student loans is about 40% (study) of requests.
Todd Zywicki posted on the Volokh Conspiracy:
But that would be the effect–you wouldn’t be able to borrow money to go to college any more. As my old friend Marcus Cole ably explained to the Senate a few weeks back when this issue was proposed. The problem, of course, is that the moral hazard and adverse selection problems here are extreme: when most people graduate from college they are massively insolvent.
The point here being that nearly every student is in deep debt at the end of college and has no tangible assets that can be seized. So every student is in a situation that would be helped by a discharge bankruptcy. Contrast that with a mortgage, where debt may be high but at least there is a property that can be seized against the debt.
To make this worse, we have the adverse selection and moral hazard problems. These mean that people who intend to declare bankruptcy can borrow more money than people who don't. People who don't can only borrow as much money as they can reasonably pay back. People who do can borrow as much as they need (moral hazard). After all, it's not like they're planning on paying it back.
Under these circumstances, there is no incentive to offer loans. The largest loans will default and discharge in bankruptcy. Since the principal is much higher than the interest rate profits, this means that such loans lose money. So the banks raise interest rates. This makes the loans more expensive to pay back, causing legitimate borrowers to withdraw. But those not intending to pay the loans don't care and stay (adverse selection).
The Brookings Institution published an argument by Rajeev Darolia that mischaracterizes this position:
If private student loan debtors were behaving opportunistically pre-policy, we would have expected a sharp relative decline in bankruptcy filings after the 2005 provision impeded their alleged opportunistic behavior, as compared to debtors whose incentives were not directly affected by the nondischargeability provision. Yet, we do not find evidence of such a reduction.
However, that's not what they say. They don't say that bankruptcy was a problem. What they say is that the threat of bankruptcy was the problem. If true, we'd expect to see loan amounts increasing after 2005. And according to the NYU Journal of Law and Liberty Blog, that's what we do see:
According to the Consumer Financial Protection Bureau, in 2013, student loan debt was over $1.2 trillion: now, the number is likely much higher. Student loan debt has ballooned since 2008, and is the only type of consumer debt that continues to go up, rather than down. Not only that, but delinquency has doubled over the last six years. Roughly a quarter of all student debt is at least three months in arrears.
Of course, something else happened in 2008 that might cause more people to seek debt and more people to struggle with paying it. Teasing out the separate effects might take longer.