Color Republicans unimpressed.

There are far fewer Republicans in Democratic districts now than there were Democrats in Republican districts in 2010, and many of the current batch of Republicans have been shored up through redistricting. More Democrats are also retiring from both chambers than Republicans; in the Senate, seven Democrats have decided to leave, the most recent being Ben Nelson of Nebraska, whose announcement last week further hurt his party’s chances of holding onto control there.

What is more, Republicans often cite the respected political expert Charlie Cook, who points out that only once since World War II has the party holding the White House gained more than 15 House seats in a presidential election year. And Mr. Obama remains an impediment in many crucial districts.

“House Democrats’ public chest-thumping is recurring entertainment,” said Representative Pete Sessions of Texas, who is Mr. Israel’s counterpart at the National Republican Congressional Committee. “But it falls far from political reality. Even Democrats know that the Republican majority is strengthening as more Democrats throw in the towel in order to avoid facing a referendum election on their job-destroying policies.”

Republicans and others also argue that the president’s new strategy of running against Congress carries risks for Democrats who could be tarred along with Republicans.

But Democrats hope that by narrowing their majority in the House, even if Republicans win control of the Senate, they can push back against the policy agenda that Republicans have pressed, often with great success, over the last year.

In any event, the political complexion of the 113th Congress will almost certainly complicate the agenda of whoever is in the White House come January 2013.

“What will most likely happen is you will either have a narrow majority in either chamber or a still-divided Congress,” said Julian E. Zelizer, a professor of history and public affairs at Princeton University. “You are looking at a president who is going to face the same governing environment that President Obama faces and Bush before him faced, and in some ways the problems might be worse.”