President Obama is hearing an earful from union allies who accuse him of chipping away at the deficit on the backs of federal employees, underscoring the political gamble he just took in proposing a two-year freeze on federal pay.

Voter enthusiasm in the Democratic base was a challenge for the president's party in the last election, and the fight Obama picked Monday with powerful unions didn't help that relationship any. Unions, who command influential get-out-the-vote operations and account for millions in fundraising dollars, are charging the president with clamping down on the middle class for the sake of a proposal that cuts into the deficit by a fraction.

"Cutting federal employee pay is really going to do nothing for the deficit," John Gage, president of the American Federation of Government Employees, told Fox News Radio. "It just looks like a panic gesture."

Gage called the amount "peanuts," arguing in a statement that a "VA nursing assistant making $28,000 a year or a border patrol agent earning $34,000 per year" should not be the target of "political scapegoating." According to the administration, the starting salary for a Border Patrol agent is actually $38,619.

Other union leaders, including AFL-CIO President Richard Trumka and National Federation of Federal Employees President William Dougan, piled on. Democratic congressional leaders expressed skepticism about the plan. Once the hubbub settled, the president's biggest backers ended up being congressional Republicans who viewed the pitch as an endorsement of the kind of cutback they've been demanding for months.

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But Democratic strategists said Tuesday that Obama ultimately has more to gain than lose out of his pay freeze plan. Strategist Joe Trippi compared the fiscal discipline posturing to former President Bill Clinton's strategy after his party's 1994 midterm wipeout -- a strategy that paid off with his reelection victory two years later. The more Obama rankles the base, he said, the more credibility the president regains with independents.

Democratic strategist Bob Beckel said the unions will bellow but that political realities will prevent them from abandoning Obama.

"They'll talk a tough game now ... but in the end they're about to face a Republican House of Representatives which has got not an inch of interest in helping unions anywhere," Beckel said. "Their choices are pretty limited here."

Trippi, though, said the unions are still capable of causing problems for congressional Democrats considering signing on to Obama's pay freeze proposal. They could put pressure on wavering members, he said, and threaten a primary challenge if they don't budge.

Obama said Monday that the two-year freeze on civilian federal pay would save $2 billion this fiscal year and $28 billion over the course of the next five years. House Republican Whip Eric Cantor, R-Va., called the plan "exactly the kind of savings measure we have to make in order to begin to restore some fiscal sanity in America."

But two high-ranking Democratic congressman, who happen to represent Maryland districts packed with federal workers, cast doubt on the proposal.

"By focusing exclusively on federal employees, the administration runs the risk of reinforcing the myth, pushed by some for politically convenient but cynical reasons, that America suffers from a federal government comprised of unproductive and overpaid civil servants. Nothing could be further from the truth," Rep. Chris Van Hollen, D-Md., said in a written statement, calling the pitch a "piecemeal approach."

House Democratic Leader Steny Hoyer, D-Md., said the plan would have produced "significantly more savings" had military personnel been subject to the same freeze.

Obama exempted members of the armed forces from his proposal.