The White House on Wednesday chimed in on the GOP's spat over presidential candidate Newt Gingrich, saying it shows that Medicare could define the 2012 campaign.

In a rare tweet about the 2012 GOP primary field, White House communications director Dan Pfeiffer wrote

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The White House's comment is the latest sign that Democrats are looking to hammer Republicans on Rep. Paul RyanPaul RyanRyan: Graham-Cassidy 'best, last chance' to repeal ObamaCare Ryan: Americans want to see Trump talking with Dem leaders Overnight Finance: CBO to release limited analysis of ObamaCare repeal bill | DOJ investigates Equifax stock sales | House weighs tougher rules for banks dealing with North Korea MORE's (R-Wis.) budget proposal on the campaign trail.

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Ever since the House passed Ryan's budget in April, Democrats have sought to tie Republicans to it, accusing them of wanting to privatize Medicare.

Republicans say the so-called "premium support" proposal in Ryan's budget, which would give seniors a voucher to choose insurance from private providers, will help keep the program solvent over the long-term.

Democrats' focus could also turn to other likely GOP presidential candidates who have praised Ryan, but said they will offer their own Medicare reform plans, such as former Massachusetts Gov. Mitt Romney and former Minnesota Gov. Tim Pawlenty.

But in the meantime, Democrats have focused on GOP infighting over Gingrich's comment that Ryan's plan to restructure Medicare is an example of "right-wing social engineering."

The remark has dominated the headlines and provoked anger from other top Republicans, including House Majority Leader Eric CantorEric CantorEric Cantor offering advice to end ‘immigration wars’ Trump's olive branch differs from the golden eras of bipartisanship After divisive rally, Trump calls for unity MORE (R-Va.), South Carolina Gov. Nikki Haley (R) and Ryan himself. 

Over the past few days, Gingrich, the former House Speaker, conducted damage control to alleviate tension between himself and other Republicans. He emailed and called Ryan on Tuesday to apologize for his criticism.

"I made a mistake. And I called Paul Ryan today, who's a very close personal friend and I said that," Gingrich told Fox News's Greta van Susteren. "The fact is that I have supported what Ryan has tried to do on the budget."