"That medical bill could be the difference between being credit-worthy and not credit-worthy," said Dvorkin.

The proposed measure could have widespread ramifications. In the last two years, 57% of the people who lost jobs that offered health insurance have become uninsured, according to a recent Commonwealth Fund study.

In 2010, 30 million adults were contacted by a collection agency for unpaid medical bills. Meanwhile, an estimated 44 million Americans said they were actively paying off medical debt in 2010, the study found.

"Medical debt is not a reliable indicator of credit risk, yet nearly a quarter of Americans have seen their credit scores plummet because of small, routine medical bills," said Rep. Nydia Velazquez (D-NY), a co-sponsor of the bill.

However, opponents of the bill -- including some lenders and credit reporting companies -- argue that removing medical debt from credit reports takes away an important factor in determining risk used in lending decisions.