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Both sides say the cuts will lead to massive layoffs, particularly among defense contractors, who said that under federal law they’ll be required to warn their employees of job losses 60 days ahead of time — which happens to be just days before the election.

The Obama administration issued guidance this week saying those warnings aren’t necessary, but Republicans said the law is clear and accused the president of trying to hide job losses from the public in the run-up to voting.

None of the choices is particularly palatable to a majority in Congress: Raise taxes to cover $110 billion, cut spending elsewhere to make up for the money, or just cancel the cuts altogether — which would mean deepening the deficit and passing on the cost to future taxpayers, with added interest.

Add to that the debate over the Bush tax cuts, where the two sides are equally stalemated.

Republicans’ tax plan, which calls for a one-year extension of all current rates in order to give Congress breathing space for a broader tax overhaul, cleared the House on Wednesday. But last week Senate Democrats passed a version that allows tax rates to rise for households making $250,000 or more.

The Senate vote was 51-48, barely squeaking by with no Republican support.

That compared to the House GOP proposal, which passed easily and garnered support of 19 Democrats from conservative-leaning parts of the country. One Republican, Rep. Timothy V. Johnson of Illinois, voted against his party.