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President Obama seemed to be coaxing Republicans back to the negotiating table by offering to change the inflation adjustment in Social Security and other government programs -- but his offer also has had the unwanted side effect of riling many of his supporters on the left.

As the White House delivers its 2014 budget proposal to the Hill Wednesday morning, grumbling on the right about the budget's increased taxes is almost outdone by the complaints on the left about the Social Security change, which activists say will cut benefits. The liberal group Campaign for America's Future claims it has collected two million signatures from people opposed to such changes to entitlement programs, and delivered the petition to the White House on Tuesday.

Roger Hickey, the group's co-director, calls Obama's move "really bad policy and bad politically for the Democratic Party. So we are sending a message that Democrats had better not vote for this," he told Fox News.

What the president proposed is to shift the inflation adjustment for federal programs from a broad measure of the Consumer Price Index to a more narrow one called the "chained CPI," which Hickey dismisses.

"This is a camouflage operation designed to easily -- they think it's going to be easy -- to cut government expenditures across the board and they hope people won't notice," Hickey said.

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    Supporters of such a change, however, say the chained CPI is based on a simple premise, that people change their purchases depending on prices.

    "When the cost of one good goes up by a lot, we shift into another good," said Maya MacGuineas of the Committee for a Responsible Federal Budget. "If apples become more expensive, we'll buy a couple more bananas. So the chained CPI is a more accurate measure of inflation."

    The change would only reduce future increases in benefits by .25 percent a year, according to the non partisan Congressional Budget Office. But over 10 years, it would lower the deficit by $339 billion.

    That's because the change in the CPI wouldn't just be for Social Security, but for all federal programs adjusted for inflation, including federal pensions and tax brackets.

    "This is a government-wide chain CPI," Doug Holtz Eakin, a former director of the Congressional Budget Office, said. "And as a result, that is how you get the tax increases, that's how you get the Social Security impacts, but you also get the other pension impacts."

    A chained CPI would increase taxes by pushing people into higher tax brackets sooner than the current measure of inflation would.

    The Obama administration, which will release its annual budget plan Wednesday, says the money it saves in Social Security will be kept within the program, to help sustain it when it starts to run short of money in the early 2030s.

    But liberal groups question the necessity.

    "It's almost like taking a whack out of Social Security as a way of symbolizing our ability to do something," Hickey said.

    And in the eyes of deficit hawks, entitlement reform still would have a long way to go.

    "This is $340 billion over 10 years," Holtz Eakin said of the money raised by the switch to the chained CPI. "We'll spend $10 trillion on Social Security, $8 trillion on Medicare, $6 trillion on Medicaid. So we are not in the ballpark of the kinds of changes we need to really fix these programs."

    With with social security, "the trustees tell us every year the program is unsustainable," MacGuineas said. "You need to make changes now so that we can phase them in gradually."

    And less painfully, because small changes made now can make a big difference two or three decades from now.

    The CPI shift would save $127 billion in Social Security. By law, the program can only pay out what it takes in. And in 2033, it will have to reduce benefits an estimated 25 percent across the board -- a potentially crushing blow for the poor.

    The system's actuaries say even the change in the CPI will move that date back by only two years.