Did Scott Walker change his position on immigration (again)?

Wisconsin Governor Scott Walker speaks at the American Action Forum January 30, 2015 in Washington, DC.

Win McNamee, Getty Images

Wisconsin Gov. Scott Walker once supported a path to citizenship for citizenship for some undocumented immigrants living in America. Then he changed his mind, voicing his opposition to a path to citizenship. Now, the Wall Street Journal reports that Walker is again voicing support for a path to citizenship -- a charge his team disputes.

During a private Republican dinner in New Hampshire on March 13, Walker said he supports allowing undocumented immigrants to remain in the U.S. and eventually become eligible for citizenship, three people present at that dinner told the Journal.

Walker, during his remarks, reportedly mocked 2012 Republican nominee Mitt Romney's position that undocumented immigrants should "self-deport." He said those immigrants, rather than being deported, should be able to " eventually get their citizenship without being given preferential treatment."

That statement is directly at odds with Walker's most recent public position on the subject - a reversal that could handicap his political ambition as he prepares to launch a 2016 presidential bid.

Walker spokesman Kirsten Kukowski, though, said Thursday that the Journal's report is simply wrong.

"We strongly dispute this account," she said in a statement. "Governor Walker has been very clear that he does not support amnesty and believes that border security must be established and the rule of law must be followed. His position has not changed, he does not support citizenship for illegal immigrants, and this story line is false."

For much of his time in public life, Walker said he would support a path to citizenship for some undocumented immigrants, given certain conditions and penalties.

"Sure, yeah. I mean, I think it makes sense," he told the Wausau Daily Herald in 2013.

But when he was pressed on that question by Fox News' Chris Wallace earlier this month, Walker said he'd changed his mind after talking with border-state governors about the need for more border security and stricter enforcement of immigration laws.

"My view has changed. I'm flat out saying it," Walker explained. "Candidates can say that; sometimes they don't."

Over the following weeks, Walker continued touting his opposition to "amnesty" - a label many conservatives have attached to the idea of granting citizenship to residents of the U.S. who are in the country illegally.

At an event in Concord, New Hampshire on March 14, Walker explained, "This is one where we listened to the people all across the country, especially border governors who saw how this president messed that up...And that's an issue where I think where people want leaders who are willing to listen to people."

But the night before, at the private dinner, Walker was singing a different tune.

"He said no to citizenship now, but later they could get it," Bill Greiner, a restaurant owner who attended the dinner, told the Journal.

Walker said undocumented immigrants should "get to the back of the line for citizenship," added Franklin, New Hampshire Mayor Ken Merrifield, who was also at the dinner.

Walker's alleged waffling underscores the dilemma facing the Republican Party as 2016 approaches: The GOP base strongly opposes a path to citizenship for undocumented immigrants, and candidates who disagree can expect stiff resistance from the conservative grassroots in a primary battle.

But the party's more business-friendly establishment wing has been generally supportive of immigration reform efforts, including a path to citizenship, arguing that it's not only good policy, but also a smart political move that that will help a Republican win the general election