When the Obama administration included in its fiscal 2014 budget proposal a plan that would effectively reduce Social Security benefits over the years, officials braced for a strong backlash from Democrats and other defenders of the entitlement program.

The White House certainly got an earful from fellow Democrats, but the idea also is drawing sharp resistance from the right, and that is creating an unlikely coalition of opposition from very different sides of the political spectrum.

That’s because along with shifting to a stingier way of calculating annual cost-of-living adjustments for federal entitlement programs, use of the chained consumer price index also would set a new inflation gauge for the tax code. That would slow increases in tax bracket thresholds, meaning individuals would pay more in taxes as their income grows faster than inflation.

The Congressional Budget Office says that would bring in almost $124 billion more in tax revenue over the next 10 years than current law.

“If you know what it is, and you’re a Republican, you should be against the tax increase part of it,” said Grover Norquist, president of Americans for Tax Reform. The icon of the anti-tax movement argues the proposal would unravel the indexing of tax brackets that took effect in 1985 under President Ronald Reagan.

President Barack Obama included the idea in his budget proposal as part of a larger bid to bring Speaker John A. Boehner, R-Ohio, into a broad deficit reduction plan.

Although Boehner has praised the move, some rank-and-file Republicans, such as Tom McClintock of California, say Norquist’s opposition adds to doubts about the idea. “I’m not wild about the chained CPI,” McClintock said. “It artificially pushes taxpayers into higher brackets, which increases their effective tax rate.”

Although there is debate among economics researchers about chained CPI, it has one clear appeal to politicians: As a technical adjustment to an inflation measure, it would effectively lower Social Security benefit increases without requiring lawmakers to vote directly for reduced benefits.

The Bureau of Labor Statistics’ conventional inflation measure tracks monthly price changes among some 80,000 goods and services that researchers say represent average consumer spending. Proponents say chained CPI is more realistic because it incorporates changes that prices cause in consumer behavior — switching from steak to chicken, for instance, when beef prices rise.

The CBO says the chained CPI advances an average of 0.25 points slower than the conventional CPI on an annual basis. That small difference would compound over time, the CBO says. Social Security benefit payouts would shrink by $127.2 billion from 2014 and 2023 and overall federal spending would fall by $216 billion over that time.

But Obama says the offer to use chained CPI on entitlements does not stand alone, and applying it to the tax code means tax brackets would grow more slowly every year. Taxpayers who see their incomes grow more rapidly would fall into higher brackets, leading to $123.7 billion in more tax revenue through 2023.

For now, Norquist says the proposal would violate his group’s long-standing no-tax-increase pledge because it is not offset by tax cuts. “Even if it were revenue neutral, we would probably oppose it,” he said.

He urged Republicans to look for other ways to curb entitlements and called for the outright deletion of the tax-related portion of the chained CPI proposal.

Robert Greenstein, president of the liberal Center on Budget and Policy Priorities and a defender of Obama’s proposal, suggested that likely would knock the offer entirely off the table.

“If the tax portion is deleted, I will move from support to vigorous opposition,” he said.

Although the tax increase is relatively small, Norquist and other tax activists contend it would grow over time and hurt many taxpayers. He and other conservatives suggest tax adjustments should be pegged to wage growth, not consumer prices, to erase “bracket creep” that comes when incomes grow faster than inflation.

But for lawmakers still interested in a long-term deficit reduction deal, the two-sided effect of chained CPI represents the trade-offs they believe they will have to make to reach a final agreement.

Sen. Rob Portman, R-Ohio, said Obama’s move to make the chained CPI a part of debt talks reassured Republicans he is serious about trying to slow the growth of entitlements. Portman said the chained CPI proposal was likely to be included in any deal, if one can be reached, despite opposition on the left and right.

“It’s an important first step,” Portman said. “As part of an overall plan, I can support it.”

Rep. Steve Scalise of Louisiana, chairman of the Republican Study Committee, said that although he shares concerns about the tax-related effects of the chained CPI, the plan could move as part of a broad tax overhaul that would meet terms of the no-tax-increase pledge and satisfy conservatives.

“I won’t speak just to chained CPI, because any kind of tax reform we would be doing would be a combination of things that would not have a net increase on taxes,” Scalise said. “In fact, what we would like to see is a net decrease in taxes.”

After discussing the chained CPI proposal in a House Democratic Caucus meeting April 11, Greenstein said Democrats are unlikely to back it unless it is combined with more tax increases. Even then, he predicted, Democrats would demand explicit assurances Republicans will not make Democrats’ support of the chained CPI proposal a campaign theme.

Norquist believes the opposition of liberals and some conservatives probably will be enough to block the chained CPI proposal. “The present House is not voting for a tax increase,” he said.

And Rep. Keith Ellison, D-Minn., a co-chairman of the Congressional Progressive Caucus, backs that view: “There’s an agreement among liberals and some conservatives. It’s not moving.”