A group of 9/11 first responders joined lawmakers in Washington on Tuesday to urge the Senate passage of a health care bill meant to provide free medical treatment to those suffering from the health effects of working in and near ground zero following the 2001 attacks.

In the years following the attacks, health experts have noted respiratory and mental health conditions, such as post-traumatic stress disorder, in those who engaged in ground zero rescue and cleanup efforts.

The bill has been in legislative limbo since Thursday, when Senate Democrats failed to win a procedural vote to open debate on it....