WASHINGTON — Democrats voted for the 13th time Tuesday to keep the federal government shut — as Senate Majority Leader John Thune told The Post there was an easy fix to ensure millions of Americans won’t lose access to SNAP program food payments.

“The simplest way to end it and the simplest way to make sure that people are getting the food assistance they need is to pick up the bill and give us five votes,” Thune (R-SD) said in an exclusive interview shortly before the Senate failed to reopen the government in a 54-45 vote.

“And we’ll, we’ll send it to the president. It’ll be signed into law,” he continued.

“Everything opens up, everybody gets paid and SNAP recipients get their benefits.”

Nearly 42 million Americans receive SNAP benefits to help them buy food, but monthly payments will not go out on Saturday because of the ongoing government shutdown, which entered its fifth week Tuesday.

The benefits, commonly known as food stamps, help about 1 in 8 Americans buy groceries using debit cards loaded each month by the federal government.  The average payment is $350 per household.

Roughly 83% of households that receive SNAP benefits include children, a disabled person, or an elderly person.

Thune anticipated that the threat to food stamps, coupled with an encroaching date for enrolling in health care insurance plans, “should” bring the shutdown to an end by the weekend, though he didn’t expect Senate Minority Leader Chuck Schumer (D-NY) to join a handful of moderate Democrats in making that happen.

“Thune seems perplexed about what precisely it is that Democrats are pushing for,” Schumer proclaimed in a floor speech Tuesday. “But he knows damn well what Democrats want — it’s the very same thing that a vast majority of Americans want, including nearly 60% of MAGA voters: We want to lower healthcare costs, now.”

At the same time, pressure on Democrats to back down is mounting. The president of the largest union of federal employees called Monday for party lawmakers to pass a stopgap funding bill on a bipartisan basis with Republicans.

Nick Daniels, who leads the air traffic controllers’ union, stopped short of fully endorsing that so-called “clean” continuing resolution to pay federal workers — but demanded that the shutdown “end today” in remarks to reporters Tuesday, according to Politico.

“I don’t know why any of this has to happen. Nobody wins in a shutdown. We’ve been saying that for a long time,” Thune said. “Right now, [their] metric of how this is going is … is it serving their political interests or not?”

“I think there are half-a-dozen Democrats out there for whom these labor unions are … their opinion and influence could be fairly consequential in terms of what they ultimately decide to do. I can’t believe it wouldn’t be,” he added.

“I hope that the consequences of this become more real over time,” the Republican leader emphasized, “there’s a couple of key deadlines coming up here and I’m hoping that will get them to come to their senses.”

The Department of Agriculture’s shutdown plan had initially included possibly using contingency funds for SNAP — but the department updated its website last weekend to indicate no benefits would be issued on Saturday as scheduled.

The USDA warned “the well has run dry” for benefits and blamed Democrats for holding up the government shutdown.

Still, only three Democrats or Democrat-aligned independents — Catherine Cortez Masto of Nevada, John Fetterman of Pennsylvania and independent Angus King of Maine — voted with Republicans on Tuesday to advance the bill that would patch up the funding.

Meanwhile, a coalition of Democratic-led states — including New York — filed a lawsuit Tuesday to stop the Trump administration from suspending food aid benefits, arguing it violates federal law.

“Millions of Americans are about to go hungry because the federal government has chosen to withhold food assistance it is legally obligated to provide,” New York Attorney General Letitia James said in a statement.

“SNAP is one of our nation’s most effective tools to fight hunger, and the USDA has the money to keep it running. There is no excuse for this administration to abandon families who rely on SNAP, or food stamps, as a lifeline. The federal government must do its job to protect families.”

But a spokesperson for the Department of Agriculture blamed the pause on Democrats refusing to break ranks with Schumer to end the shutdown.

“We are approaching an inflection point for Senate Democrats,” the spokesperson said in a statement.

“Continue to hold out for the Far-Left wing of the party or reopen the government so mothers, babies, and the most vulnerable among us can receive timely WIC and SNAP allotments.”

Despite Republicans having offered several off-ramps for Democrats to join with them in funding the military, federal workers not already furloughed and even SNAP, Thune said his leadership team didn’t anticipate them biting after several attempts.

“Plan A and Plan B are: Open up the government,” he insisted. 

Vice President JD Vance in a visit to Capitol Hill Tuesday for a lunch with Senate Republicans urged them to hold the line.