Republicans, while hopeful that most of the bad outcome will be for President Obama, largely concur. “I think that there is a palpable dissatisfaction and frustration with all of us,” said Shelley Moore Capito, a veteran Republican from West Virginia.

The poll numbers for Congress lag far behind those of Mr. Obama, who was at 46 percent approval in the latest New York Times/CBS News poll, in October, while only 9 percent of respondents approved of the way Congress was doing its job. Yet there is a big difference between Mr. Obama’s ratings and those of Congress: the president, not Congress, tends to dominate the political debate, and the party in charge tends to take the heat.

This is something many House Republicans are clinging to. “People are really frustrated by the lack of any optimism,” said Representative Eric Cantor of Virginia, the majority leader. But he blames Mr. Obama, saying, “That’s why people’s anger continues to grow, because they don’t see the leadership on his part.”

Some lawmakers wonder if members of Congress have even single-digit approval from the public. “I’d like to meet the 6 percent who approve of Congress,” said Representative Jeff Flake, Republican of Arizona, who has often voted in ways that help hold up legislation, because he is seeking deep cuts in spending. “I just don’t know who they are.”

In public forums, polls and interviews, voters have expressed disgust and frustration with the divided Congress in which so little legislative progress is made that the government nearly shut down recently over a disagreement between Republicans and Democrats over how to pay for disaster aid. The nation’s stubbornly high unemployment rate has begotten a sense of desperation among voters that seems to stretch far beyond the normal pro forma disgust with Congress.

“This election cycle is somewhat unprecedented because of these historically low approval ratings,” said Nathan L. Gonzales, an editor at The Rothenberg Political Report, a nonpartisan newsletter that rates 77 House races as competitive so far, a relatively low figure compared with 2010. “But because of redistricting, in the ways that these districts are drawn, it insulates a majority of the body from being thrown out.”

One potential result is unlikely to soothe the public. Consider the prospect that a Democratic gain of a few seats in the House or a Republican takeover of the Senate that leaves them well shy of a 60-vote majority could result in even more entrenched gridlock, not less.

“It is plausible that Republicans lose seats in the House and gain them in the Senate,” said John Sides, a political scientist at George Washington University. “Republicans would still be able to pass stuff in the House, but it would just be harder. Where they would lose seats would be in moderate districts, which would leave the conservative faction of the House gaining more power. You could get tenuous control of the Senate by Republicans, but maybe not with a 60-vote majority. So those things are just a recipe for even more challenges going forward.”