Several Senate Democrats want to eliminate a requirement in the health care law for companies to provide coverage if they have fewer than 100 workers.
The current cutoff is 50 employees, although the Obama administration has suspended the so-called small business mandate temporarily. The legislation would mean an estimated 98 percent of businesses could decline to provide insurance without fear of a penalty.
The bill is backed by five Democrats and one independent.
Three of the Democrats are seeking re-election at a time Republicans are emphasizing their demand for repeal of the law. Democratic strategists are urging their candidates to emphasize changes they would make and to stress parts they support.
The bill is part of a series of changes the group of lawmakers introduced Thursday.