The Senate measure would generally require that victims be notified of the results of rape kit tests, including any DNA matches, as well as toxicology reports that could show whether they had been given a date-rape drug, for instance. It would codify existing protections from the Violence Against Women Act that prevent victims from being charged for those exams, meaning that the right could be upheld in court.

The bill would also ensure that rape kits would be preserved without charge for 20 years or until the statute of limitations expires, whichever comes first. Statutes of limitations vary greatly: Wyoming does not have one for felony sex crimes, while the cutoff in Illinois is three years if the victim does not report the crime within that time, Ms. O’Connor said.

The fight for greater protections has played out most publicly on college campuses and in military courts-martial. And highly visible examples like the accusations against the comedian Bill Cosby — who faces trial on charges of sexual assault after a judge ruled on Tuesday that the case against him could proceed — have helped bring attention to the cause, Ms. O’Connor said.

Congress has been working its way through a handful of bills to improve the treatment of victims.

This month, the Senate Judiciary Committee approved a criminal justice bill that included a provision to eliminate the heavy backlog of rape kits awaiting testing. And Democrats on the Senate health committee, led by Senator Patty Murray of Washington, have been pressing for a bill to improve medical services for victims, including the development of the first national standards for care after assaults.

The biggest hurdle for the measures, as it has been for nearly all legislation in Congress in recent years, is the cost. Conservatives in the House have balked at most any bill that calls for new spending, as some of these would.