The Mets have a tough road ahead of them in their quest for a third World Series championship, after an up-or-down season, but their fans say, “Ya gotta believe.”

The Amazin’s face off against the San Francisco Giants in a do-or-die, wild-card game on Wednesday night, the culmination of an improbable run to the postseason, and a survey of Big Apple supporters this week found a range of emotions and expectations.

“They’re kind of playing with house money right now and they’re dangerous if they make it,” said Danny Abriano, the editor of Rising Apple and an editor at SNY, the Mets’ network. “Last year, they kind of were a runaway train. There wasn’t this one-and-done type feeling.”

This is only the second time the Mets have clinched back-to-back playoff chances — the first was the 1999 and 2000 seasons.

But they have an uphill battle ahead compared to last season’s team, which lost to the Kansas City Royals in the World Series. They’ve been plagued by injuries that have sidelined some of last year’s best, including pitchers Matt Harvey and Jacob deGrom.

Marc Sacks, 28, a Mets fan and the general manager of the midtown Modell’s at 430 Seventh Ave., said interest in team merchandise has risen (they’re getting even more inventory in on Wednesday and again Friday if they win), but it doesn’t compare to 2015.

“The excitement level is not as high as last year,” said Sacks, who lives in Bethpage, Long Island. “I’ll be excited if they win tomorrow. I think we have the Cubs number.”

Others felt similarly optimistic about the Mets’ chances against Chicago in a possible National League Division Series, despite the Cubs’ MLB-best 103 wins in the regular season.

“I think if they get past [Wednesday], they’re going to take out the Cubs,” said Jeffrey Yanover, 47, from Oceanside, Long Island. “I think they have the mental edge against the Cubs.”

Jeffrey Paternostro, a senior writer at Baseball Prospectus, said whatever happens on Wednesday, it’s been an “improbable” run so far.

“I think Mets fans never trust the Mets. Even last year when they looked really good, you’re always waiting for the other shoe to drop,” Paternostro said. “There’s always that built up cynicism.”

But it’s the playoffs, he said, so anything can happen.

“Teams have come out of the wild card and made the World Series before. It can certainly happen; really, anything can happen,” he said.

But Justin Favor, 34, said the way the season has gone is what makes the Mets the Mets.

“It’s what we’re about — gritty,” said Favor, a union organizer and laborer from Rockaway Beach. “Either way, it wasn’t a disappointing season. When the expectations are high, we do well.”

Manhattan fan Adam Gross, 21, stopped by the Mets Clubhouse Shop near Bryant Park ahead of the game, which he was attending with his family.

“Citi Field is going to be crazy,” Gross said. “It is really exciting.” (With Nick Morales)