ALBANY – Gov. Andrew M. Cuomo and legislative leaders are including in the soon-to-be-passed state budget a new system to help finance political campaigns.

They call it the “Family Tax Relief” act.

Lawmakers and the governor last week agreed to give $350 in tax relief to hundreds of thousands of households across the state. Even though they call it a tax credit, the money won’t be taken off taxpayers’ annual tax returns in the spring.

Instead, the governor and legislators will send checks of $350 apiece to residents’ mailboxes, and many expect the checks will go out shortly before November 2014. That’s when the governor and the legislators are up for re-election.

While they say the plan is about helping middle-class families with children, the governor and lawmakers hope the checks will put a smile on the face of voters that will continue beaming when they go into the voting booth.

Critics, including those who have no problem with giving tax breaks to middle-income families, say the tax rebate checks are a political gimmick that uses $350 million of taxpayer money to lure voters into supporting incumbents.

It is a point upon which left-leaning and right-leaning groups agree, and that makes for an odd day in Albany.

“Lawmakers certainly never hesitate to spend taxpayer money on their campaigns when it benefits their own re-election efforts,” said Bill Mahoney of the New York Public Interest Research Group, which has no position on the actual tax break but does have a problem with the likely timing of the program.

“In many ways, it’s a public finance program only for incumbents, and this only hurts the electoral process,” Mahoney added.

“It’s like a Publisher’s Clearinghouse check in the mail,” added E.J. McMahon, director of the Empire Center for New York State Policy, a conservative think tank. “It seems pretty obviously politically motivated. It’s meant to say, ‘I’m your friend’ to the middle class.”

The tax break will work like this: Every person or couple with at least one child up to the age of 18 and making between $40,000 to $300,000 will get the $350 check. (Albany reality check: Some lawmakers said the tax break is for families with children from 4 years to 18 years old, while Cuomo and Senate Republicans said it applies from birth to 18.)

While the measure is part of the 2013 budget talks for the fiscal year beginning April 1, the family tax break program won’t actually be counted on the ledgers until the 2014 fiscal year.

Cuomo’s office said 1.1 million New York families will get the check, including 66,000 in Erie County and 15,000 in Niagara County.

No one has said for sure when the checks will go out. But when Assembly Speaker Sheldon Silver was asked if mid-October was likely, he replied: “They might.”

“The comptroller’s up for re-election,” Silver joked.

And Comptroller Thomas DiNapoli’s signature is very likely to be on the checks.

This isn’t a new campaign strategy.

In 2006, lawmakers and then-Gov. George E. Pataki approved the STAR property tax rebate program, which distributed checks to 3.4 million taxpayers and cost the state $700 million.

The checks that year, and for the few years the program lasted, arrived at voters’ homes just before November election day. And coinciding with the checks were taxpayer-funded newsletters from lawmakers, informing constituents that the checks were on the way.

While the budget has not yet passed this year, Cuomo and legislative leaders all touted the family tax checks last week after announcing a “tentative” deal on the 2013 budget.

Senate co-leader Jeff Klein, a Bronx Democrat, described it as part of a “family-friendly” budget.

The other Senate leader, Dean Skelos, a Nassau Republican, called it a “recognition of [the] struggle” facing middle-class families in New York.

Speaker Silver, a Manhattan Democrat, said it provides “needed relief to middle-class families.”

And Cuomo said the measure is a recognition that “taxpayers have been overtaxed for too long.”

Meanwhile, Citizen Action of New York, a left-leaning group that has been pushing for a publicly financed campaign finance system in the state, had a different description.

“The rebate check is a $350 million election-year gimmick,” said Karen Scharff, executive director of the group, “aimed at giving incumbents another advantage in their re-election campaigns.”

Others have criticized it because it gives no tax break to parents with children in college, or most senior citizens, or single people or couples with no children.

McMahon, the conservative think tank director, questioned why the Senate Republicans would push such a program, especially since the GOP has only been losing senators since the STAR program was enacted in 2006.

“So, if this is a new form of campaign finance, it’s not working out well for them,” he said.

Mostly, though, McMahon said he questions the lack of any coherent and significant tax-cut program that would turn around New York’s high-tax image.

For instance, the STAR property tax program that gives large tax breaks to seniors who live in homes that many have already long paid off needs to be examined, he said.

And Cuomo and lawmakers should reduce state spending to give larger tax breaks to more residents and help localities reduce state-imposed spending mandates so they can lower property taxes, he added.

“I don’t think there is any kind of real tax policy here,” he said of the $350 check program. “It certainly has nothing to do with boosting the economy. It’s hard to see any motivation other than political,” he said.