Their position exposed a break with Senate Republicans, all three of whom on the commission supported the blueprint. That split in part reflects the different roles the Republicans will have in the House and Senate. While Republicans have picked up seats in the Senate, they remain in the minority there. House Republicans, having won a majority after campaigning as a conservative alternative to the Obama administration, say they are obligated to fulfill their vision rather than compromise. They also face pressure from the Tea Party movement, which has made slashing government spending the centerpiece of its agenda.

The commission did not formally vote because support for the plan written by the co-chairmen  Erskine B. Bowles, the president of the University of North Carolina system and a former chief of staff to President Bill Clinton, and Alan K. Simpson, a former Republican Senate leader from Wyoming  fell three votes short of the 14-vote supermajority required to send the package to Congress under the terms of Mr. Obama’s executive order that established the panel.

The 11 supporters were evenly split between the parties  five Democrats and five Republicans, along with an independent, Ann M. Fudge, the former chief executive of Young & Rubicam.

Despite that bipartisan majority, the outcome at best sent ambiguous signals about whether the White House and Congress could reach an agreement, given the political pain behind the tax and spending decisions that are required.

Several supporters said that although they backed the thrust of the plan, they would not vote for it as actual legislation given their opposition to various provisions. One such supporter was Senator Richard J. Durbin of Illinois, the second-ranking Senate Democrat and Mr. Obama’s closest Senate ally. He said the package was not balanced between spending cuts and tax increases and it took “too much away from programs that support the neediest.”

Yet even the plan’s opponents said it should serve as “a template,” in the words of Representative Xavier Becerra, a Democrat from California.

Another opponent on the panel, Andy Stern, the former president of the Service Employees International Union, said, “This plan deserves a vote, and this president needs to make sure that by the State of the Union he also has his own plan and his own leadership because this is the issue of our time that must be solved.”