The line at the Newark ticket counter took forever, but at last our boys were giddily weighing themselves on the baggage scale as we handed over our tickets to paradise: one week in Mexico for the whole family, starting on Presidents Day.

“Passports, please,” the agent said.

Beaming, my husband handed these over, too.

“Four passports,” the agent said.

That, my husband later said, is when his heart plunged. “Four?” he asked. “The kids need passports, too?”

“Since January 23rd,” the agent replied.

Next thing you know, we were in a taxi barreling back to our apartment, our cheery driver saying, “I keep getting folks like you.”

Idiots, in other words. Idiots who apparently missed the millions of warnings: “New Passport Rules Going Into Effect.” The driver was so used to folks like us, in fact, that he drove us home past 376 Hudson St., saying: “That’s where you want to go tomorrow morning. Passport office. They’ll set you right up.”

Maybe they would have. But when we reached the office by phone (877-487-2778), a recorded voice told us the next available appointment was two weeks hence. Then we called one of the private companies that specializes in last-minute passport procurement — for a price, of course — and the woman there said there was no way could she get us out fast. Her agency was totally booked up, too, thanks to the new rule that states birth certificates are no longer sufficient. Every American, even newborns, now needs a passport to fly to Mexico, Canada, or most of the Caribbean isles.

So, next thing you know, we were in the car, barreling down to Washington, D.C.

Our goal was not to picket the State Department: We were just trying to salvage a nice, little family vacation. You know — the kind with gray skies, whipping winds, and the ransom you pay for a last-minute hotel room (chilly draft, gratis).

Did the children care we weren’t headed to Mexico? Please. One got a giant penny at the Bureau of Engraving and Printing, and it was like we gave him a puppy. He rolled that penny down the D.C. sidewalks, showed it off to strangers, placed it next to his plate when he ate. Pure love. His older brother, meantime, basked in several thrilling days of candy bars for dessert. “Twix? Really? Hooray!” So, all in all, it was a fantastic trip. (We also saw the Smithsonian.)

Upon our return to reality, however, I wanted to find out if the cabbie was right — did a whole lot of idiots spend their vacations the way we did?

“Yesterday we were supposed to get on a plane to Aruba,” foot surgeon Vadim Nekritin said. I found him at Rush Passport on West 31st Street waiting to see if his trip could be saved. “We got to the airport and they said she needs a passport,” he said, pointing to his dozing 3-year-old. “‘I lost approximately $1,500 and two days of my trip.”

“How do you feel?”

“Wonderful.”

I asked for that. But then came the thrilling call, “All right! I have your passport!”

“You’re the best!” Dr. Nekritin cried, and he was off. Bon voyage.

Expediters such as Rush charge anywhere from $150 to $300 for their services. Sometimes they can get your passport in a day, sometimes they can’t. It seems to depend on whether they have any open “slots” — pre-set appointments with the regional passport agency. Mere mortals can make these appointments by phone, as we’d tried to do, or they can go to the agency in person and spend some very tense time at the phone bank in the lobby.

“Don’t call the number they say. Call the operator! Talk to a real person!” Tanya Pineda advised another hapless couple yesterday. She had just scored an appointment for later that morning, which meant she might get her passport later that day, or the next.

The State Department claims its turnaround times have not slowed down. It still takes about eight weeks if you file for a passport at your post office, spokeswoman Janelle Hironimus said, and about two weeks (unless you can prove it’s an emergency) if you go to your regional office and pay an extra $60 fast-track fee.

If, however, it turns out you’ve totally blown it and cannot take your dream vacation, consider this: Man plans, God laughs.

But when man buys a giant penny and some candy, and his children laugh, too, well — that’s what I call a pretty great vacation.