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But it's unclear if that will win him any love from either side.

Democrats who fear he'll flip his vote at the last minute are still attacking him. President Donald Trump's allies are attempting to turn him into an example of the political cost of abandoning his own party's White House, launching television ads targeting Heller on Tuesday. They later backed down after Heller and other GOP senators complained.

Senate Majority Leader Mitch McConnell's decision to delay the health care vote until after the July 4 recess means Heller will still be viewed by both sides as a potentially dividing vote -- ensuring that the pressure won't subside anytime soon.

Local Republicans, meanwhile, smell blood in the water and are weighing whether to take on Heller -- the only Senate Republican up for re-election in the 2018 midterms in a state that Hillary Clinton won -- in the primary.

Danny Tarkanian, the son of the legendary UNLV basketball coach Jerry Tarkanian, is considering a run against Heller in Nevada's Republican primary.

"A lot of people are looking to find somebody to run against Heller, so there's a lot of chatter out there," Tarkanian told CNN.

Tarkanian has run for office unsuccessfully five times in recent years in Nevada. But he has won Republican primaries four of those five times and would enter the race as an already widely known figure. He initially wanted a rematch with Rep. Jacky Rosen, who won their head-to-head House race last fall. But when news broke last week that Rosen was set to challenge Heller, that "changed everything," Tarkanian said.

He said he is "probably going to end up" running again for the House seat -- but is "not closing the door on anything."

Heller's critics in Nevada argue he could suffer from the same fate as Rep. Joe Heck in his 2016 Senate race against Democrat Catherine Cortez Masto. Heck criticized Trump in October, weeks before the election, only to back away from that criticism later once it became clear he was at risk of alienating Trump's core supporters. Heck narrowly lost the race.

Wayne Allyn Root, a conservative talk radio host, said during a radio interview Sunday he had received more than a dozen emails urging him to run against Heller in the primary -- though he said he didn't have time for such a run.

"He needs to be primaried. We can't take him anymore," he said.

Heller's office did not respond to multiple requests for comment.

The political pressure being heaped on Heller comes after a Friday news conference alongside the popular Republican governor Brian Sandoval, during which Sandoval railed against the Senate GOP health care bill, saying it would harm the 210,000 Nevadans who gained health insurance through Obamacare's expansion of Medicaid.

Sandoval provided political cover for Heller that could ease the nerves of moderates in Nevada -- if not in Washington.

But Heller was already endangered headed into the 2018 midterm elections. In 2012, Heller won less than 46% of the vote in a razor-thin Senate race. Headed into 2018, Democrats have identified him as their best pickup opportunity on an otherwise challenging map.

Heller is still facing attacks from Senate Democrats' campaign arm, Emily's List and other progressive organizations that say they do not trust him to maintain the opposition to the health care bill.

The pro-Trump super PAC America First Policies launched digital advertisements against Heller over the weekend and said it would spend a total of $1.3 million on a campaign that included television and radio ads attacking his position. In the end, it pulled the ad buy, but not before repeatedly hitting Heller for his actions.

The 30-second narrated television ad depicted Trump and Heller -- and does not mince words: "Call Senator Heller. Tell him America needs him to keep his promise: Vote 'yes' to repeal and replace Obamacare."

The Trump-aligned super PAC's decision to wade into the race -- a move that started over the weekend with a digital ad saying Heller is "now with Nancy Pelosi," a hated figure among conservatives -- crystalized the tightrope Heller must walk headed into his re-election bid.

The decision to aggressively target Heller appeared to mark a major tactical difference between Trump's allies and Senate Republican leadership.

McConnell called White House chief of staff Reince Priebus over the weekend to express his displeasure, a source familiar with the call told CNN Tuesday.

Texas Sen. John Cornyn, the No. 2 Senate Republican, told CNN's Manu Raju, "I think the more constructive thing for me to do is to continue to talk to my friend and colleague and convince him that this bill is not perfect, but it is much better than the status quo and it is also much better than a meltdown of the Obamacare exchanges, which will put million of people at risk."

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Sharks circle around Republican Sen. Heller in Nevada - CNN