President Barack Obama on Tuesday floated the idea of making it easier for student borrowers to get rid of some of their student debt through the bankruptcy process.

Thirteen Democrats in the Senate acted on that suggestion Thursday when they introduced a bill dubbed the Fairness for Struggling Students Act of 2015 that will treat student loans issued by private banks the same as other types of private unsecured debt in bankruptcy proceedings.

At the moment, it’s nearly impossible to wipe out student loans in personal bankruptcy; it’s only allowed in extremely rare circumstances. That’s thanks in part to a change in the federal bankruptcy code in 2005 that shielded private loans from being discharged in bankruptcy. A similar protection for government-issued or guaranteed loans had been in place since 1978. The bill introduced Thursday seeks to reverse those 2005 changes so borrowers can once again get rid of private loans in bankruptcy.

“Too many Americans are carrying around mortgage-sized student loan debt that forces them to put off major life decisions like buying a home or starting a family. We can no longer sit by while this student debt bomb keeps ticking,” Senator Dick Durbin, a Democrat from Illinois and a co-sponsor of the bill, said in a statement.

To be clear, if the bill defies the long odds it faces in a Republican-controlled Congress and becomes law, it will cover only a small chunk of student loans. Private banks issue about 10% of all student loans and only those would be eligible for discharge in bankruptcy. The federal government issues the remaining 90% of student loans and they would remain relatively untouchable.

Even still, the Consumer Financial Protection Bureau pegs total student loan debt at $1.2 trillion—more than the nationwide balances for credits cards and auto loans—or about $30,000 per student on average. Of that, $165 billion stems from private loans. Student loans made by banks are an obvious target for the Obama administration because they often lack the lower interest rates, consumer protections, and repayment options that accompany loans issued by the government. In 2012, at least 850,000 private student loans equaling $8 billion were in default, according to the CFPB.

The new bill is the latest in a series of efforts by the White House to address the nation’s ballooning student debt. The Obama administration is also planning to set up a system in which borrowers can lodge complaints against loan servicers. In June, it announced an expansion of a federal program aimed at lowering student loan payments.

The Consumer Bankers Association, the lending industry’s primary trade group, responded to Obama’s proposal to allow the elimination of private loans in bankruptcy by pointing out that less than 3% of private loan borrowers are in “financial distress.” It encouraged lawmakers to address the rising costs of college instead.