It’s a case that smacks of small-time corruption, with allegations of cash payoffs in parked cars. But the charges a Democratic state senator schemed to bribe his way into the GOP race for New York City mayor are playing out on a big political stage.

The case has already created political quicksand for Republicans just as the mayoral race is heating up and might have a second act in Albany, where the investigation is reviving corruption as a hot-button concern after Gov. Andrew Cuomo campaigned on pledges to rout it out.

“What it really does is make political corruption a much bigger issue than it has been” in the mayor’s race, while upping pressure on Cuomo and other state leaders to do more to thwart it, said Paul Moses, a Brooklyn College English professor and former journalist who specializes in writing about New York City government and politics.

Good-government advocates held news conferences at both City Hall and the state Capitol Wednesday, a day after state Sen. Malcolm Smith, City Councilman Daniel Halloran, two high-ranking city Republican Party officials and the mayor and deputy mayor of suburban Spring Valley were arrested in a multi-pronged federal probe.

At the heart was Smith’s yen to run for the Republican mayoral nod, despite being a Democratic member of the state Senate leadership.

While that might seem odd, a number of longtime Democrats have sought waivers or switched parties over the years to try to get the Republican ballot line in the mayor’s race, rather than join a Democratic field that’s usually more crowded with experienced politicians. And while Democrats dominate voter registrations and many city offices, none has held the mayor’s seat in 20 years.

Federal prosecutors said Smith arranged to pay tens of thousands of dollars to two Republican officials to get waivers allowing him to try to get on the ballot as a Republican. Halloran, a Republican, got paid to help line up the illicit deals, prosecutors allege. Through their lawyers, both lawmakers have denied the allegations.

Smith is the latest in a string of state politicians who have faced corruption prosecutions in recent years, prompting Cuomo’s 2010 campaign vow to clean up Albany. Steps so far have included cutting individual grants lawmakers direct to nonprofits and pushing through a law that allows for legislators to lose their pensions for committing felonies related to their jobs.

Yet on Wednesday, Cuomo wondered aloud about the persistence of the problem.

“Why do people continue to do things when they know it’s wrong, it’s illegal and they’re going to get into trouble? That’s the great riddle,” he told reporters in Oswego.

Smith has come under scrutiny before. In 2010, New York’s inspector general examined his and other legislative leaders’ role in giving a video slot machine contract for the Aqueduct racetrack to a consortium that was later disqualified. Investigators said Smith continued advocating for the contract award after he said he recused himself. The report was referred to federal and city prosecutors, but no one has been charged.

Smith was seen as quite unlikely to get the mayoral nomination and never actually launched a campaign for it. Nonetheless, the alleged scheme has rippled through the Republican side of the race.

The GOP operations in two of the city’s five boroughs are in upheaval, since Bronx Republican Party Chairman Joseph Savino and Queens Republican Party Vice Chairman Vincent Tabone both were arrested. Republican mayoral candidate John Catsimatidis quickly jettisoned Tabone as a campaign consultant and suspended him from his job as a lawyer for the billionaire candidate’s businesses.

Another GOP mayoral hopeful, former Metropolitan Transportation Authority Chairman Joseph Lhota, distanced himself from backers he’d welcomed only weeks ago. Lhota said Wednesday that neither Savino nor Halloran, who both had endorsed him, would have any further role in his campaign.

The case is “a stain on the Republican Party,” Lhota said by phone, but “I think it portends nothing for the race.”

Leaders of the five borough parties didn’t immediately respond to phone and email inquiries Wednesday, while state Republican Chairman Ed Cox urged Savino and Tabone to resign from their party offices.

With Democratic voters outnumbering Republicans by more than 6 to 1 in the city, mayoral elections provide local GOP leaders a key opportunity for influence — and fundraising. And some observers suggest the latter takes on an outsized role.

When Republican mayoral candidate George McDonald met with the borough Republican leaders last summer, “they weren’t interested in message — they were just interested in how much money” he could generate in donations to the party, McDonald recalled Wednesday. McDonald, who runs an organization that helps the homeless, said he didn’t expect the party leaders’ support and so wasn’t affected by the turmoil.

On the Democratic side of the campaign, mayoral candidate Bill de Blasio seized on another part of the corruption allegations: charges that Halloran took additional bribes in exchange for promising to allocate a company up to $80,000 in City Council “discretionary funds,” or money that each member controls. It usually goes to nonprofit groups in the member’s district. De Blasio called for banning discretionary funds, misuse of which has previously led to criminal convictions of three council members.

Halloran ran for Congress last year, losing to state Assemblywoman Grace Meng days before her father, former Assemblyman Jimmy Meng, pleaded guilty to wire fraud. Halloran brought up the case against the elder Meng during the congressional race, eliciting a stern response from his opponent’s campaign.

Halloran is now running for re-election to his council seat.

Whatever effect the corruption charges have on politicians and parties, they also may add to the cynicism of an electorate that is all too accustomed to seeing such cases, said Christina Greer, a Fordham University political science professor.

“This just reinforces what so many voters think is already going on,” she said.

(AP)