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Democrats are unlikely to muster the two-thirds vote needed in the Senate for the constitutional amendment, much less win support in the House and in the states for getting it ratified.

Likewise, they fell six votes shy of the 60 needed to overcome the filibuster on the tax bill Thursday.

Only one Republican, Sen. Mark Kirk of Illinois, voted with Democrats, who also were hurt by several absences among their own troops.

The tax cut package would extend, for two more years, a series of breaks that benefit certain groups such as teachers who spend their own money on school supplies and college graduates with student loans. The package also includes continued breaks for wind turbines and for research and development.

The $85 billion cost is not offset, meaning it would significantly deepen the deficit lawmakers have worked so hard to cut.

The House is working on a different set of tax breaks, making a half-dozen of them permanent, at a cost of more than $300 billion over the next decade. Those, too, are not offset.

Republican aides predicted that the Senate would return to the tax breaks bill before the end of the year.

Both the House and Senate bills would test President Obama, who has pushed for higher taxes as part of a “balanced” approach to the deficit.