When the House of Representatives roll was called Jan. 19, only three Democrats joined with House Republicans in voting to repeal the new health law. This development was notable in that it meant most of Democrats who voted against the overhaul the first time around, and were reelected to Congress in November, voted not to repeal it this time — evidence that they may be sensing that support for the health overhaul hardening. A quick examination of public opinions offers evidence as to why this idea might be taking hold.

First off, recent polls have shown public perception of the overhaul may be improving. Although the country is still evenly divided in its overall feelings toward the new law, a recent Washington Post-ABC News poll found that less than one in five want the whole thing repealed. Similarly, a Kaiser Family Foundation poll released the day of the President’s State of the Union address found that, though about half of Americans remain opposed to the measure, most aren’t as supportive of repealing, replacing or defunding it as congressional Republicans are. (KHN is a program of the Kaiser Family Foundation.)

Another recent poll, this one by Fox News, found only 27 percent of those asked wanted the whole law repealed while 34 percent wanted parts of it repealed and 20 percent wanted it expanded. And within Fox’s collection of numbers, one specific finding jumped out. Only one in seven of those polled by Fox News want the health law to remain as it is. In other words, for now at least, the country seems to be settling on “fix or improve” attitude toward what we have.

Backed by findings like these, Democrats in Congress seem just as convinced defending the bill is a winning issue as Republicans are certain they have the high ground in trying to scrap it.

But what do voters want in the run-up to the 2012 elections? Cooperation.

A recent USAToday poll found that 80 percent of those asked said the President Barack Obama and the Republicans should work to pass legislation they can agree on — even 70 percent of Democrats agreed with that. Eighty-three percent said that it is extremely important for House Republicans to pass legislation that both parties agree on — including 77 percent of Republicans.

More than another bitter and protracted health care debate in 2011, what Americans want the Congress to focus on is policies that will lead to more jobs. While I expect a number of House committees to hold lots of health care hearings in the next few months, I also expect Republicans to begin to move on to other issues rather than spend the whole year on health care.

Back home, most House Democrats are not on the defensive over the new health care law. But that is not always the case with Senate Democrats. With a disproportionate number of their seats in play in 2012 — and with Sen. Kent Conrad, D-N.D., already deciding not to run again — it will be the Senate Democrats up for reelection who most want to look like they are being the constructive ones. The individual mandate may be one of the areas on which they focus their attention.

My sense is that what many Americans, particularly swing voters, want to hear most about health care is that Democrats and Republicans found a way to work together to make the new law better — not repeal it, but not leave it as it is either.

Ironically, I expect it will be these vulnerable Democratic senators, not Republicans who still think they have a winning issue bashing the new law, who will be the most eager to fix or improve the measure.