WASHINGTON — The White House says President Barack Obama is setting a goal of lowering the deficit by $4 trillion over the next 12 years as he wades into the politically volatile debate over the nation’s crushing debt.

A week after formally announcing his re-election campaign, Obama is set to propose a mix of tax increases already rejected by Republicans, and cuts to safety-net health programs likely to alienate many liberals.

In a speech today at George Washington University, the president also is expected to propose reducing defense spending and eliminating tax breaks and loopholes.

Obama’s plan falls well short of the more than $5 trillion in cuts over a decade proposed by House Republicans, and dismissed by Democrats as draconian.

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