Kate Steinle Murder at Center of Immigration Debate in DC

As the family of a woman allegedly slain by an undocumented immigrant filed a claim today in advance of a lawsuit over her death, a fierce debate in Washington over the practice of so-called "sanctuary cities" is expected to consume Congress after members return from their summer recess.

Congress has been working on legislation known as "Kate's Law," after Kate Steinle, the victim of the attack in San Francisco that made national headlines earlier this summer. It would end federal funding for so-called sanctuary cities that defy federal immigration actions.

San Francisco, where Steinle was killed, is one of those cities, which is why the Steinle family filed a claim against the city's sheriff, Ross Mirkarimi, as well as the U.S. Bureau of Land Management and U.S. Immigration and Customs Enforcement.

"The system failed our sister," Brad Steinle, Kate's brother, said at a family news conference today, fighting back tears. "And at this point nobody has taken responsibility, accountability. And nothing has changed."

Two months since Kate's murder in early July at San Francisco's Pier 14, the bill that bears her name is still stalled in the Senate Judiciary Committee. A staff member for Senate Judiciary Committee ranking member Sen. Pat Leahy said the Senate would take it up when lawmakers return from recess, but Beth Levine, a spokeswoman for Republican Chairman Chuck Grassley said that the committee is also exploring other options because "the Democrats have not indicated a willingness to help pass legislation." She did not elaborate.

The House is considering companion legislation, introduced by Rep. Matt Salmon of Arizona.

"Kate's Law" would bar sanctuary cities from accessing more federal grants than are already available to them and increase penalties for individuals who re-enter the United States after deportation. It's not clear how much bipartisan support the bill would receive -- a similar bill passed the House in late July, with the votes divided largely along party lines.

The case is also figuring heavily on the presidential campaign trail. Donald Trump released a video on Instagram featuring images of undocumented immigrants accused of murder, including Francisco Lopez Sanchez, the convicted felon who allegedly killed Kate Steinle, juxtaposed with Jeb Bush calling illegal immigration "an act of love."

The parents of Kate Steinle have found themselves at the center of the sanctuary cities debate.

Jim Steinle testified before the Senate Judiciary Committee in July, urging lawmaker to pass legislation like Kate's Law that would keep undocumented immigrants like Sanchez, a convicted felon who had been released from prison, from remaining in the country.

"Our family realized the complexity of immigration laws. However, we feel strongly that some legislation should be discussed, enacted or changed to take these undocumented immigrant felons off our streets for good," Jim Steinle said.

ABC News' Avery Miller contributed to this report.