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WASHINGTON — The Senate’s border proposal was one of the toughest bipartisan bills to emerge on the issue in decades. Yet it quickly collapsed when Republicans — galvanized by Donald Trump, the likely Republican presidential nominee — rejected the compromise as insufficient.

Now Democrats see an opening.

Senate Majority Leader Chuck Schumer called Trump’s rejection of the border legislation “a gift” for Democrats and said they plan to “constantly over the next year” remind voters that it was Republicans who torpedoed the deal. And he says the strategy has already paid dividends, with Democrat Tom Suozzi, who campaigned on tougher border enforcement, winning a special election this week in New York, flipping a House seat away from Republicans.

Schumer said the race in his home state of New York “says something very significant — that border is no longer the province of Republicans.”

That calculation is already having far-reaching effects, transforming the way President Joe Biden and Democrats talk about one of the biggest issues in this year’s elections and shaping the policy debate over immigration.

It’s a strategy with significant political risk. Republicans have campaigned on border security for years, and public frustration is running high with the record number of illegal U.S. border crossings. While arrests for illegal border crossings dipped by half in January, they reached 249,735 in December, the highest monthly tally on record. Cities, including many run by Democratic mayors, are straining under an influx of migrants.

Republicans pin the historic number of illegal border crossings directly on Biden and argue that the Senate legislation would not have been enough to curb it. They say Democrats are only trying to excuse away their own failures.

Sen. John Cornyn, a Texas Republican, said earlier this month that the influx of migrants “burdening my state and a lot of the major cities around the country is unsustainable and has proven to be a political liability for President Biden, so they want to try to act like they’re doing something about it for a fig leaf.”

Democrats, trying to cling to a thin Senate majority and retake the House, are undeterred. They see the spectacular collapse of the bill as a cautionary tale for voters and another way to tie GOP candidates to Trump, especially in swing races.

“Republicans aren’t willing to stand up and solve issues,” said Rep. Suzan Delbene, a Washington Democrat who chairs the party’s House campaign committee. “They are led by the most extreme members of their party and when Donald Trump says he doesn’t want to move something, they all fall in line.”

That message is aimed at a group of voters that will likely be crucial in the election — swing voters and the minority of Republicans who do not like Trump.

“If we could show Democrats were serious and Republicans were not interested or rejected doing border, it would help neutralize the issue, which was a loser for us,” Schumer said.

Now that the House is considering the $95.3 billion foreign aid and national security package that had previously been paired with the border policies, some members have once again considered adding border security measures to the package. Schumer was open to again considering border policy, saying “Our main job here is to get something done.”

But House Speaker Mike Johnson, R-La., said Wednesday he would not consider anything similar to the Senate bill because “it did not meet the moment, it would not have solved the problem.”

Trump has openly bragged about defeating the Senate’s border proposal. He’s argued that it would have allowed in “millions” of migrants because it included a provision that would have expelled migrants without allowing them to apply for asylum only after Border Patrol encounters became unmanageable for authorities.

The senators who crafted the bill, including Republican Sen. James Lankford, have said Trump’s claim about the bill is not true.

At the same time, Biden has embraced some of the terms that Trump used about border enforcement as he pressed Congress to take up the bill, which would have overhauled the asylum system with tougher standards and faster enforcement.

Speaking at a political event in South Carolina last month, Biden said he would have used the Senate bill to “shut down the border until it could get back under control.”

Putting the strategy into motion, the campaign arm for Senate Democrats is launching a blitz of ads attacking Republicans for voting against the border enforcement bill — even taking the fight to Texas, where Sen. Ted Cruz is seeking another term.

Cruz has taken aim at Republican Leader Mitch McConnell for blessing the deal, arguing that it was “spectacularly stupid” to negotiate with Democrats.

Cruz’s likely Democratic opponent, Texas Rep. Collin Allred, said he’s already talking about the border deal on the campaign trail. He said he’s had issues with the Biden administration’s approach, but he thought the Senate negotiators “arrived at a pretty constructive place.”

“This is a very real issue for Texans,” Allred said, “and a senator who doesn’t want to solve it.”

The potency of immigration as a campaign issue was evident in the New York special election.

On suburban Long Island, Lois Clinco said she voted for Suozzi Tuesday in hopes he would prevent migrants from settling in Levittown, a town some 30 miles from New York City. She was concerned about safety amid the many migrants arriving in New York City — and the increasingly dire rhetoric from city officials about violence and crime.

“I’m hoping that he keeps our area, our area and keeps the migrants out,” the 59-year-old Clinco said. “We’re overpopulated now and with schools and everything else, it’s just a difficult time.”

Many Democrats, faced with historic numbers of migrants coming to the southern border and cities whose resources are overwhelmed by the influx, have also warmed to the idea of tougher border enforcement.

“Immigration and the situation at the border is one of the last high profile issues where Republicans have a powerful narrative,” said Connecticut Sen. Chris Murphy, who was the chief Democratic negotiator on the border policy. “So even blunting the political advantage that they think exists on the border could be the difference between winning and losing.”

Still, immigration advocates and progressive lawmakers worry that Democrats could leave immigrants behind if the party fails to champion the economic and social benefits they bring to the United States.

Rep. Ro Khanna, a California Democrat who is a surrogate for Biden and had joined him in South Carolina, said he disagreed with the president’s rhetoric on “shutting down the border.” Khanna pointed to how past Democratic presidents from John F. Kennedy to Barack Obama described immigrants as contributing to the country.

“We have adopted a frame that starts with blaming immigrants as part of the problem,” he said. “We need to shift that frame to celebrate what immigrants have done for America.”

Advocates for immigration are also cautiously looking at the shift. Todd Schulte, the president of FWD.us, an organization that supports immigration reforms, agreed that Democrats needed to go on the offensive by drawing a contrast with Trump, but also called for them to craft proposals that address “a failed” immigration system.

“Draw a contrast, but then you have to deliver on policy,” he said.

Murphy agreed that Democrats should remain committed to broad immigration reforms, including pathways to citizenship for migrants who are already here. But he argued that may only be possible once Democrats first show voters they are serious about tough border enforcement.

“We have to read the writing on the wall, our belief as a party that we could do it all at one time has simply proven not to be true,” he said.