CORRECTION: A previous version of this post misidentified Rep. Julia Brownley’s district as that of former representative David Dreier, both of whom represented California’s 26th Congressional District. Under the redrawn map that took effect in 2012, Brownley’s district is most closely aligned with that of former representative Elton Gallegly.

House Republicans believe they can expand the field of battleground seats in the November midterm elections, following the struggled rollout for President Obama’s new health-care law and his own sagging popularity.

Despite signs that barely one in 10 House seats are competitive, the National Republican Congressional Committee recently commissioned polls in four Democratic seats that are not currently on any political strategist’s radar, finding Obama deeply unpopular in several districts with a normal tilt toward Democrats.

“Republicans have the opportunity to expand the playing field and stay on offense in 2014,” Liesl Hickey, executive director of the NRCC, wrote in a memo provided to The Washington Post. “As a result, our recruitment efforts are ongoing, and we see a real opportunity to run competitive races in these districts.”

Democrats reject that the race will be about Obama and health care, saying the Republican brand and its record-low approval ratings will be a heavier counterweight for GOP candidates. “We have to make this a referendum on solutions and bipartisanship,” Rep. Steve Israel (N.Y.), chairman of the Democratic Congressional Campaign Committee, said in a recent interview.

Republicans, however, are betting that the drag from Obama and the implementation of the Affordable Care Act will outweigh their party’s own brand issue. For example, of the four districts that the NRCC polled in, one was Israel’s own on Long Island, which Obama won in 2008 by 8 percentage points and by 3 percent in 2012. Now, the president’s approval rating is upside down in that district, 39 percent approving and 52 percent disapproving of his job performance, according to the NRCC surveys done by Harper Polling.

In the Ventura County-based district of freshman Rep. Julia Brownley (D-Calif.), just 38 percent of voters approve of Obama’s performance while 52 percent disapprove. One of Brownley’s potential opponents is in a statistical dead heat with her. It’s a district that was previously represented by a Republican for 26 years but was dramatically redrawn in 2012, prompting the GOP incumbent, Elton Gallegly, to retire after regularly winning re-election with about 60 percent of the vote.

In the new district in 2012, Brownley won by more than 5 percentage points and Obama won it by 10 percent.

GOP strategists expressed shock at some of these numbers. “They will all be forced to run with an unpopular president spouting an unpopular agenda,” Hickey wrote.

The data suggests an electorate that is even more restless than most strategists have previously realized. However, the redistricting process during the 2012 election cycle has left so many House seats in safe terrain that even the most optimistic Republican estimate would be a gain of only about 10 seats, or a couple more, if the current political environment stays in place until November. That’s a far different outlook than in 2010, when Republicans picked up 63 seats on election night, or over the 2006 and 2008 elections, when the Democratic waves netted more than 50 seats combined.

At the moment, independent analysts rate barely 50 seats in contention for November – 24 Democratic, 28 Republican, according to the Rothenberg Political Report – and all signs have pointed toward a status quo midterm election, with either side picking up fewer than a handful of seats.

Israel, who does not have a serious opponent, said that he counts 10 recent GOP retirement announcements as potential pickups for Democrats, vs. just three Democratic retirements that he acknowledges will be possible Republican gains. He said he does not expect candidates to play defense on the health law and would instead focus on “candidates who are about solutions”, trying to pin public disgust with congressional crises and brinkmanship over the past three years on the House’s GOP majority.

Still, several months of bad headlines from the ACA rollout have lifted Republican spirits to a place that seemed unthinkable in mid-October, after the 16-day shutdown of the federal government sunk GOP fortunes to new lows. Last week at the House Republican retreat on Maryland’s Eastern Shore, Rep. Greg Walden (Ore.), the NRCC chairman, practically guaranteed that his party would gain seats in November. Yet Walden noted that the “field is narrower” than in previous cycles, for his rationale in assuring reporters that the GOP was not in danger of losing the majority.

Now Walden’s advisers contend they can put some seats in play that don’t show up on battleground lists from Rothenberg or the Cook Political Report. Here are some of the results of the four Democratic districts that the NRCC polled in, conducted by Harper polling in late January:

Julia Brownley, CA-26 (PVI, D+4)
Generic Ballot
GOP: 45%
Democrat: 42%

Jeff Gorell/Julia Brownley Head to Head
Gorell: 44%
Brownley: 42%

Brownley Job Approval
Approve: 32%
Disapparove: 32%

Brownley Reelect
Deserves reelection: 32%
Someone else: 42%

Obama Job Approval
Approve: 38%
Disapprove: 52%

Steve Israel, NY-03 (PVI, D+2)
Generic Ballot
GOP: 43%
Democrat: 42%

Steve Israel Job Approval
Approve: 37%
Disapprove: 27%

Israel Reelect
Deserves re-election: 33%
Someone else: 36%

Obama Job Approval
Approve: 39%
Disapprove: 52%

Open, NY-21 (PVI, EVEN)
Generic Ballot
Republican: 46%
Democrat: 34%

Obama Job Approval
Approve: 32%
Disapprove: 55%

Suzan DelBene, WA-01 (PVI, D+4)
Generic Ballot
GOP: 46%
Dem: 43%

Suzan DelBene Job Approval
Approve: 34%
Disapprove: 32%

DelBene Reelect
Deserves reelection: 36%
Someone else: 39%

Obama Job Approval
Approve: 40%
Disapprove: 51%