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Mr. Obama also has called for $50 billion in new infrastructure spending, as well as another year of the 2 percentage point payroll-tax cut and emergency unemployment benefits — both of which are scheduled to expire at the end of the year.

House Republican leaders delivered a counteroffer last week that included $800 billion in new taxes, which they derived from eliminating loopholes in the tax code. The plan called for a lower inflation measure to be used to calculate Social Security benefits and $900 billion in cuts to projected entitlements spending — though they have been vague about which programs would be affected.