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“Now is not the time to send the kind of mixed message that it sends when we are working with our allies to achieve the goals that we believe that are widely shared in Congress,” he said.

Democrats who supported Mr. Obama accused Republicans of trying to damage the president for political reasons, and said the vote is squandering a chance to change perceptions of the U.S.

“We have the opportunity to show the Arab world and every nation of Earth who we are as a people,” said Rep. James P. Moran, Virginia Democrat. “It shouldn’t matter who is in the White House.”

A bipartisan group of senators is also moving to bolster the president.

Senate Foreign Relations Committee Chairman John F. Kerry and Sen. John McCain, the ranking Republican on the Armed Services Committee — and coincidentally, the last two losing presidential candidates — have joined forces to write a resolution backing Mr. Obama’s limited war.

Their resolution largely mirrors the first measure the House defeated Friday, though, suggesting that even if the House or Senate passes something, it will face a tough time getting through Congress as a whole.

With a legislative stalemate possible, Mr. Kucinich is pursuing a court strategy as well. Earlier this month he led a bipartisan group of lawmakers in suing to halt the deployment, arguing Mr. Obama is violating the 1973 War Powers Resolution.