An unprecedented effort to persuade some 10,000 plaintiffs who responded to the World Trade Center terror attacks to accept a $712.5 million settlement of their respiratory illness claims is nearing the finish line.

Firefighters, police and cleanup workers who toiled in the pit at Ground Zero face a filing deadline today to opt in to the settlement, and the lead plaintiffs’ lawyer said last week that he expects to meet the 95 percent participation level required to make the settlement effective.