Cross your fingers: Mayor Bill de Blasio might’ve finally gotten the message about the need to reclaim the subway.

After two vagrants turned up dead on trains, NYPD Chief of Department Terence Monahan vowed Tuesday to send 1,000 cops plus outreach workers into the system during Wednesday’s station-closings to clear things out. That, Hizzoner insists, will “disrupt” the problem of the homeless turning the subway into private shelters, endangering everyone’s health and safety.

It’s “absolutely the right thing to do to ensure the subways are safe and clean,” de Blasio said. Monahan noted that test runs saw cops lure “around 20” vagrants a night to shelters or hospitals.

Closing stations will be rough on some riders, but if it lets the city restore the system, it may be worth it. Alas, it’s a big “if.”

What happens, for example, if they refuse to leave — or do so only when cops forcefully close a station? And how does the mayor stop these squatters from returning just hours later?

The city shouldn’t slap Band-Aids on the problem. It needs strong, consistent, continuous enforcement, so the homeless and riders alike clearly know: The subway is reserved for transportation — not housing.