Democrats and Republicans in the Senate have joined forces to propose a law they say will help fix a problem experienced by at least 40 percent of Americans — surprise medical bills.

Surprise medical bills are frequently the result of patients receiving treatment from a health care provider that they didn't know was not covered by their health insurance. In a bill they will introduce to the Senate Thursday, co-sponsors Democrat Maggie Hassan of New Hampshire and Republican Bill Cassidy of Louisiana want to make health care providers negotiate these out-of-network charges with the insurance companies before billing the patient.

"What Maggie and I advocate," said Cassidy, who was a practicing gastroenterologist before entering the Senate, "is that, OK, let's hold the patient harmless and let these other entities work it out."

Said Hassan, "It's called baseball-style arbitration. It's been piloted and used well in New York."

If the insurance company and the health care provider can't reach an agreement, the bill stipulates that an independent arbiter would step in and choose a price for the provided service based on the market rate in the state.

"Baseball-style arbitration" got its name from Major League Baseball, where players can choose to arbitrate their salary instead of accepting what their team offers. The player and the team name their numbers, and then an arbiter picks one of the numbers.

Nicole Briggs had an emergency appendectomy. Because she didn't know her surgeon was out-of-network, she got a surprise medical bill for almost $5,000 that resulted in a lien on her home and her salary docked by 25 percent each month. Ray Farmer / NBC News

In 2015, the state of New York passed a bill modeled on baseball's system. It went into effect two years ago. As of March, it had been used to settle about 2,000 disputes, according to Vox. A Yale study showed that both the number of out-of-network bills and the price of emergency room care had fallen in New York since arbitration was introduced. New Jersey passed a law similar to New York's in 2018.

Four out of 10 Americans, according to a recent poll, said that they have received surprise medical bills in the past year.

Cassidy and Hassan say they have the bipartisan support to pass their bill, which has multiple sponsors from both parties. Said Cassidy: "This is not a Democrat or Republican issue. It is an American issue."