The third graphic that will rotate through the billboards says “NY Pass The Child Victims Act,” a piece of proposed legislation in Albany that would give victims until age 28 to file criminal charges and allow them to sue until age 50. It would also create a one-year “lookback” window, during which cases from any time could proceed in court. Today, the statutes of limitations in New York that govern the sexual abuse of children are among the most restrictive in the country. Most adult survivors had until they were 23 years old, at the latest, to bring a case.

Activist groups have been pushing the Child Victims Act in Albany for more than 10 years, and have made an especially aggressive effort this year, targeting specific state senators. Ms. Sullivan moved to New York City last month from her home in Florida to help lobby for the measure.

Supporters are trying to make the act part of the state budget, which is due April 1 — a tactic that would give Gov. Andrew M. Cuomo, who supports the bill, more leverage to negotiate with legislators. The Child Victims Act has support from the State Assembly, which is controlled by Democrats, but there is resistance to it in the Republican-controlled State Senate, which has blocked the bill for years. John J. Flanagan, the Senate majority leader, did not respond to questions about the legislation.

A central sticking point is the lookback window. Cardinal Timothy M. Dolan, the archbishop of New York, said on Tuesday that any legislation that included it should be rejected and called the window “toxic” for the Catholic Church. Representatives of the church have said it supports changing the statute of limitations, but fears a flurry of lawsuits and the financial hit a lookback window might deliver.

But proponents of the legislation have said that hasn’t happened in states that have enacted similar legislation, and they call the window crucial. In addition to providing victims their day in court, they said the window serves a public-safety function by flushing out suspected abusers who are still in the community.

“The lookback window will help identify abusers, many of whom still have contact with kids,” said State Senator Brad Hoylman, Democrat of Manhattan, who sponsored the bill in the Senate. “New York has among the worst laws in the country on child sexual abuse. We are an outlier, so this fix is a long time coming.”