Bracing for a one-on-one battle with Donald Trump, Ted Cruz is trying to dispense with Marco Rubio by choking off his path to the nomination in New Hampshire.

On Tuesday, Cruz went out of his way to exploit Rubio's Achilles heel: his support for a comprehensive immigration bill in 2013, opposition to which has become an animating force of the Republican base.

“Open gates and open immigration could very well destroy our republic,” a man told Cruz on the second day of his four-day New Hampshire blitz, at a family-owned food and convenience store in Center Barnstead called the White Buffalo Trading Post.

Cruz didn’t hesitate to agree. “You are exactly right,” he said.

Then he went in for the kill.

“Let’s take the issue of amnesty. Everyone today says they’re against amnesty—well, except for Marco. But the rest of them all say they’re against amnesty,” Cruz quipped, drawing laughter. (In fact, Rubio is running ads saying he opposes “amnesty,” but he remains open to a path to citizenship for undocumented immigrants after illegal immigration is under control, which some conservatives define as amnesty.)

“In 2013, Barack Obama and Harry Reid and Chuck Schumer, joined by a whole bunch of establishment Republicans, including Marco Rubio, pushed a massive amnesty plan that would have granted amnesty to 12 million people here illegally, that would have failed to secure the border, that would have enabled President Obama to bring even more Syrian refugees to this country. Now that was a moment where every Republican could decide where he or she stood,” Cruz said as attendees nodded along. He chose the side of “millions of Americans fighting to stop amnesty, to secure the border, to keep this country safe,” he said.

A Cruz victory would be very difficult in the Feb. 9 New Hampshire primary, where Trump leads by double-digits in nearly every poll. He's placed a greater emphasis on the Feb. 1 caucuses in Iowa, where he had a 3-point edge in the latest Bloomberg Politics/Des Moines Register Iowa Poll

But Cruz doesn’t need to win in New Hampshire. Just placing ahead of Rubio has the potential to inflict a fatal wound on the campaign of the Floridian, who is stuck in third place in RealClearPolitics' national Republican poll average, behind Trump and Cruz. Rubio allies worry that without a strong finish in New Hampshire, the state where moderate GOP voters traditionally make their stand, he may fade early.

Cruz benefits from the fight for New Hampshire's large bloc of establishment-friendly voters between Rubio, Chris Christie, Jeb Bush, and John Kasich. Recent polls show that each of them, along with Cruz, has a shot at second place. For Christie, Bush, and Kasich, the challenges amplify greatly afterward, given their limited appeal to more conservative voters in states such as South Carolina and Nevada, along with Southern states that vote on March 1. Ousting Rubio in New Hampshire would mean dispatching a serious threat before the main event.

The Rubio campaign was prepared to counter Cruz. Two young volunteers stood at the entrance of Cruz’s event on Tuesday, braving freezing weather to distribute leaflets full of opposition research aimed at undercutting Cruz’s assertion that he’s a “consistent conservative.” They noted Cruz's swift turn from wanting to expand legal immigration to wanting to cut it. As Cruz stepped out of his campaign bus, one of the men waved a sign that read “Ted Cruz: Political Calculator,” and the volunteers handed out actual calculators to make their point.

Rubio himself arrived in the Granite State on Wednesday for a campaign swing that included a speech at the statehouse about his vision to “save the American dream.” The pro-Rubio super PAC Conservative Solutions is running ads in early primary states attacking Cruz as a “calculated” politician.

A one-two finish by Trump and Cruz in the first two contests could quickly turn the Republican primary into a two-man race. The Texan is laying the groundwork for that match-up. After ripping into Rubio on immigration, Cruz launched an unprovoked attack on Trump over the same issue, saying he was “absent from the field of battle” when it mattered during the 2013 debate.

“There are candidates in this race who are talking a lot about immigration now. Donald Trump, my friend—he’s been talking. Listen, the last couple of days he’s been getting rattled, he’s been throwing insults my way,” Cruz said. “But in 2013, the Rubio-Schumer Gang of Eight bill passed the Senate, and Republican leadership planned to take it up and ram it through the House.”

“For anyone who cares about the issue of amnesty, who cares about border security, that moment was the rubicon, it was the battle right there and then,” he said.

After a long pause, he added, “Mr. Trump was nowhere to be found. Did not engage in the battle. Said nothing.”

YouTube: Ted Cruz Attacks Marco Rubio & Donald Trump on Immigration

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