The state-run MTA has New York pols in a tizzy, wondering if the transportation authority can open the Second Avenue Subway on time next month, as promised.

They should stop worrying — or worry about more important things.

It really doesn’t matter whether the first three stations of the subway open in December or January, or February. What matters is that the pols still don’t have a plan to build the rest of the line, to ease the strain on our people-crushing transit system.

Last week, MTA chief Tom Prendergast sounded . . . uncertain. “We’re working very judiciously to meet this date,” he said.

But the subway can’t open until it passes safety tests. Plus, contractors are still putting in escalators and elevators. The MTA is so desperate to finish on time that it might skip one station on its first run.

The MTA is rushing because it doesn’t want to anger Gov. Cuomo by blowing this deadline. New York has been waiting for a Second Avenue Subway since 1920.

In 1922, the city’s police commissioner said that “tearing down the Second Avenue elevated line” — the El, which ran the length of Manhattan from the Bronx border to City Hall — “and constructing a subway in its place would make that street available for handling heavy traffic that originates in Brooklyn.”

By 1930, the stock market crashed. But people didn’t know yet that they were in a Depression. That year, real-estate investors optimistically noted that the far east side of Manhattan was a good bargain, because “the Second Avenue Subway route will connect the region with The Bronx on the north and the business and financial district on the south.”

New York tore down the El, and the city has the heavy traffic from Brooklyn. And the city built plenty of buildings on First and Second avenues.

But we never got our subway. The Depression did eventually intervene, halting construction. Forty years after that, the city’s fiscal crisis prevented a revival. We were broke. Plus, why build a train, when everyone wanted to live in the suburbs?

It wasn’t until Mayor Mike Bloomberg came along that the city broke ground on the project again, in 2007 — just before the economic crisis.

The three initial stations would cost $3.8 billion, and be done by 2013. Three stops wasn’t much, but no worries: “Officials vowed today to make sure the full line is built” to downtown, The New York Times reported at the time.

So: We’re already late — not just funny-joke-about-the-1920s late, but three years late in the current version. And we’re over budget. Not much, but still: The three stops between 96th and 72nd streets have cost $4.5 billion.

More important, though, is that it’s all we have: three stations, to dump people off in the same old Midtown transit system that’s now so crowded it’s losing passengers to bicycles and Uber.

In a rational world, while the MTA was slowly but steadily building its three stations, the governor and the mayor would have been planning and funding the next three stations.

That way, the day the MTA cuts the ribbon on the first three stations, it could start building the next three stations. The goal would be to get the whole line to downtown built sometime in the next decade, which seems reasonable after nearly a century.

In real life, the MTA has barely started planning for the next three stations northward. It will spend $535 million on design and preliminary work in the next three years, and expects to get $500 million from the feds for early construction work.

But most of the project — the MTA doesn’t have a cost estimate yet — “will be funded in future capital programs,” the MTA says. That is, well after 2020 — meaning we won’t be getting another three stations for well more than a decade.

As for how to pay for Phase 2? Last week, the MTA announced fare hikes — but even with that extra cash, it already faces a $319 million deficit in 2020. And that’s if things go well.

When the MTA does open up the three stations soon-ish, it’ll be an achievement. It is something, and something is better than nothing.

Five years from now, though, no one will remember whether the stations opened in December 2016 or February 2017. They will notice that they still don’t have the rest of their promised subway line.

Nicole Gelinas is a contributing editor to the Manhattan Institute’s City Journal.