Gov. Chris Christie’s plan to use straight talk to fight his way back into the 2016 Republican presidential primary has already hit its first snag.

On Tuesday, the New Jersey Republican proposed reducing or cutting Social Security benefits for future retirees who continue to earn money, an idea known as means testing. Under his plan, Social Security checks would be reduced for those who earn more than $80,000 a year in retirement and ended for those who earn more than $200,000.

Christie has framed the proposal as a much-needed burst of truth-telling on America’s entitlement programs. But it has already drawn criticism from some influential conservatives as a roundabout tax on upper-income Americans.

“Is it not, a straight-out wealth tax,” influential conservative radio host Hugh Hewitt asked Christie Tuesday. “It’s a tax on people who accumulated wealth during their life, or inherited it, they might not have earned it, they might have inherited it, but it’s a straight out wealth tax, right?”

Christie defended the plan to Hewitt, saying, “What it is, is a recognition of the fact that this program needs to provide first and foremost for those people who need retirement security the most.”

Taxes are a tricky issue for Christie owing to his record as governor. Despite a no-new-taxes pledge as a candidate in 2010, he cut property tax breaks for many New Jersey residents shortly after taking office to close a budget shortfall—effectively increasing their rates. He also raised fees for many state services.

Asked by a reporter Wednesday whether he would be open to raising any revenues at the federal level, Christie said he would listen to all proposals.

“Listen, I think we need to change the tax system significantly,” he said, adding, “As I’ve said in New Jersey, I always consider everything. Everything is on the table for conversation. But I don’t think that the problem right now in America is that we are under-taxed.”

But even his openness to considering revenue increases puts him outside GOP orthodoxy, where signing the Americans for Tax Reform “Taxpayer Protection Pledge” pledge has become the norm. Christie has not signed the pledge, according to a database maintained by the group. (He’s not alone. Former Florida Gov. Jeb Bush has also said he would not sign the pledge, drawing criticism from some conservatives who are still unhappy about his father’s record as president.)

It also breaks with recent history. In 2012, all of the Republican presidential candidates unanimously pledged to veto any deficit reduction plan that raised new revenues, even if 10 times the amount taken in was cut from the budget.

Christie has not exactly endorsed the idea of raising taxes, but for some conservatives, anything but all-out opposition signals squishiness on the issue. Still, he framed his thinking on the issue as more straight talk.

“I am a guy who is always willing to listen to anybody, but let me be clear, I don’t believe the problem we have in America right now is that we’re under-taxed,” Christie repeated. “And so the fact of the matter is when you’re a leader, you have to be willing to listen to everybody’s ideas, but my ideas, I’ve laid out very specifically how to fix the programs, which doesn’t include raising taxes. That’s not the way to fix this problem.”

Americans for Tax Reform President Grover Norquist defended Christie Wednesday in an email to TIME, praising him as a acolyte of President Reagan.

“To date Christie has opposed and vetoed all tax hikes in New Jersey,” Norquist said. “Reducing a benefit is not a tax hike. Shame on any conservative who confuses spending cuts and tax increases. For a Northeast Republican he is very Reaganite.”

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