Steinle and his wife told host Bill O'Reilly the measure would be a good way to keep their daughter's memory alive. O'Reilly is collecting signatures for a petition supporting the proposal, which would impose a mandatory five years in federal prison for people who are deported and return, and 10 years for people caught a second time.
"We feel the federal, state and cities, their laws are here to protect us," Jim Steinle said. "But we feel that this particular set of circumstances and the people involved, the different agencies let us down."
Liz Sullivan said she hopes some good might come out of her daughter's death.
"You want to make it so much better for everybody in the United States that this, as you say, would never happen again," she said.
Supporters of sanctuary protections have jumped on O'Reilly and others, saying they have politicized the death. They say public safety is improved when immigrants can work with local police without fear of deportation.
To that, Jim Steinle said, "We're getting a little tired of the finger-pointing, and we want to see some action."
Steinle's death has fueled a national debate on immigration, with advocates of stricter border control denouncing San Francisco as a city whose immigrant "sanctuary" protections harbor people who are in the country illegally. Even some prominent Bay Area Democrats say Lopez-Sanchez should have been turned over to Immigration and Customs Enforcement.
Federal records show Lopez-Sanchez had been deported three times before being sentenced to about five years in federal prison in 1998. He had finished his third stint in prison for re-entering the country illegally when he was sent to San Francisco March 26 to face a 1995 drug charge.
The San Francisco District Attorney's Office declined to prosecute, given the age of the case and the small amount of marijuana involved.
The San Francisco Sheriff's Department released Lopez-Sanchez on April 15, declining to honor a request by federal immigration authorities to keep Lopez-Sanchez in custody for 48 hours until they could pick him up for deportation proceedings.