Former congresswoman Stephanie Herseth Sandlin would defeat Rep. Kristi Noem in a rematch of their 2010 race, according to a poll released Tuesday by a Sioux Falls polling firm.

The Nielson Brothers Polling Labor Day Survey found Herseth Sandlin would defeat Noem 58 to 37 percent, with 5 percent undecided, if they met again in 2012.

According to the poll, if matched against an unnamed, generic Democrat, Noem leads 59 to 25 percent. The other 16 percent of respondents were undecided.

Josh Shields, Noem’s communications director, paid little heed to the poll in a comment he issued Tuesday night.

“Rep. Noem is focused on the job South Dakotans elected her to do by fighting to stop burdensome EPA regulations on farm dust and creating more certainty for small businesses and job creators,” the statement read. “There will be a time for politics, but that time hasn’t come yet.”

Shields has called and e-mailed The Daily Republic in recent days, asking when the poll would be released and casting doubt on the accuracy of Nielson Brothers Polling.

“We are concerned that South Dakotans are getting bad information from a suspect organization,” he said Tuesday.

Paul Nielson, a partner in NBP, said the firm has released its polling procedures.

“We actually have done that,” Nielson said in an interview with The Daily Republic. “We did make them public in the General Election last year. We’re not against showing them. We’re willing to talk with anyone.”

Republicans have been skeptical of Nielson Brothers Polling because of its ties to Democrats in the state.

Paul Nielson ran for the Legislature as a Democrat in 2006 and 2008, losing both times.

The firm conducted independent tracking polls on nine of the final 10 days of the 2010 South Dakota governor’s race and showed a closer race than any other poll.

Democrat Scott Heidepriem’s 2010 gubernatorial campaign manager, Steve Jarding, cited the polls during the closing days of the race. Daugaard, a Republican, defeated Heidepriem 61.5 percent to 38.5 percent on Nov. 2.

NBP correctly predicted Daugaard would win the election, as did all other polls, and Paul Nielson said there was a late surge toward Daugaard. He said he’s aware NBP has received a great deal of heat for the gubernatorial poll.

“We have various theories. That was one race in our polling that jumped all over the place,” Nielson said.

They feel voters were discouraged at the end from other polls that showed a large lead from Daugaard and that may have suppressed the Democratic vote, he said.

“All we do is we put the numbers out as they come to us,” Nielson said.

Nielson Brothers also projected the winner of every other race in the state last year that it polled on, including ballot questions. It gave Noem a 2-point lead in its final poll, which was her margin of victory. The poll also showed 6 percent support for independent B. Thomas Marking, which was proven correct.

NBP also polled the June Rapid City mayoral race and was accurate in its findings.

Paul Nielson said in the hypothetical Noem-Herseth Sandlin race, women seemed to shift their support to the Democratic former congresswoman, who was defeated in her bid for a fourth full term.

He said the support Herseth Sandlin received can be tied to her strong showing in the 2006 and 2008 races, which she won in landslides.

Herseth Sandlin declined to comment Tuesday on the poll.

She was in South Dakota earlier this month but is now spending much of her time in Washington, D.C., where she works as a lobbyist, as does her husband, former Democratic Texas congressman Max Sandlin.

Noem, a Republican from rural Castlewood, defeated Herseth Sandlin, who has a house in Brookings, 48 to 46 percent on Nov. 2. The independent candidate, Marking, of Custer, received 6 percent.

Most South Dakotans approve of the job Noem, 39, has done in her first year in Congress, the poll reports.

The Nielson Brothers poll shows her with a 55 percent approval rating.

“A majority of South Dakota voters approve of Representative Kristi Noem’s job performance, and say they will vote for her against an unknown Democratic candidate,” Paul Nielson said in a news release.

“However, Representative Noem is defeated by former congresswoman Herseth Sandlin in a head-to-head contest. In gaining a majority of support, Herseth Sandlin picks up large percentages of Democrats and independents.”

Among respondents, 23 percent strongly approve and 32 percent somewhat approve of Noem’s work. Another 45 percent of voters disapprove of Noem’s performance (16 percent somewhat and 29 percent strongly disapprove).

Noem’s approval numbers are 5 percent lower than Gov. Dennis Daugaard’s 60 percent approval in the same NBP Labor Day Survey.

In the race against an unnamed Democrat, Noem has the backing of 65 percent of Republicans, 53 percent of Democrats and 55 percent of voters who said they are independents or belong to other parties.

Compared with her support against a generic Democrat, Noem’s support among Republicans when pitted against Herseth Sandlin declines by 10 percentage points, from 65 percent to 55 percent.

Among Democrats, Noem’s support drops from 53 percent to 19 percent. Among independents and members of other parties, Noem’s support falls from 55 percent to 22 percent.

Against Noem, Herseth Sandlin receives 78 percent support from Democrats and 39 percent support from Republicans.

The survey was conducted from Aug. 31 to Sept. 2, according to the firm, and 470 registered voters responded to the question about the contest between Noem and Herseth Sandlin.

The question has a margin of error of 4.52 percent, at a 95 percent confidence level, according to NBP.

Minutes after the poll was released Tuesday, the South Dakota Democratic Party issued a news release trumpeting Herseth Sandlin’s lead. The release also included a copy of the Nielson Brothers Polling news release.

“Voters don’t have a case of buyer’s remorse,” said Ben Nesselhuf, chairman of the South Dakota Democratic Party. “They have a full blown case of buyer’s depression.

“Noem has clearly become part of the problem in Washington that voters elected her to fix. And as this poll shows, voters don’t want to give her another chance.”

Shields said Noem will not focus on the poll results.

“The mandate that she takes the most seriously is the one she got last November,” he said. “She’s focused on representing South Dakotans.”

Paul Nielson and his brother, Mark, are Mitchell natives who graduated from Mitchell High School and Dakota Wesleyan University. They have said the Labor Day poll was conducted independently, but was mixed with other questions asked on behalf of clients.

Paul Nielson said they were very surprised by the numbers they discovered and expect them to raise eyebrows across the state.

“We think it will,” he said. “I think it’s a surprise.”