The withdrawal of 20,000-40,000 U.S. troops from Iraq this fall would greatly help Republican chances in the November election, Rep. Mark Souder (R-Ind.) said at a fundraiser Thursday at the National Rifle Association.

Souder acknowledged in his remarks that the war in Iraq has dampened support for Republican candidates but added that withdrawing 30,000 troops could have a big impact, said Martin Green, Souder’s spokesman.

The congressman said it would amount to an “‘October Surprise’ in its effect, although he dismissed the idea that a U.S. troop withdrawal would begin for domestic political reasons.

A new Gallup poll released yesterday showed that Bush’s approval rating reached 34 percent, a new low, and that on average his approval rating has been dropping one point a month over the past four years.

Souder said that plans to withdraw 30,000 soldiers from Iraq had been previously stated, so the term “surprise” only referred to how such a move could quickly change the political environment, which most polls and experts view as anti-Republican.

“It’s a surprise in terms of a move that could impact elections because it would show progress in the war,” Green added.

Souder said that Republicans wanted to show progress in Iraq because the issue has become a liability for the party. He emphasized that the primary goal is to get as many Iraqi soldiers trained as possible so that they can fill in for departing U.S. troops, according to sources at the fundraiser.

The conservative Indiana lawmaker visited Iraq in March with House Intelligence Committee Chairman Peter Hoekstra (R-Mich.) and Reps. John Shadegg (R-Ariz.) and Dutch Ruppersberger (D-Md.).

About 130,000 U.S. service personnel are stationed in Iraq. It is unclear if some of those troops will be withdrawn, but senior military officials have said they hope to reduce that number below 100,000 by the end of the year if the insurgency does not worsen and if Iraq makes more political and military progress.

Seventy U.S. soldiers and Marines were killed in Iraq in April, making it the deadliest month of the war.

“Right now there is a real concern of where things are going. People have real questions in terms of what the outcome will be,” said GOP pollster Dave Winston.

Gen. George Casey, the commander in Iraq, told reporters last week that the Iraqis’ agreement on a prime minister “certainly is a major step in the process” of reducing troop levels. But he added that more political progress is required to make a recommendation on a drawdown of troops.

“There is no October Surprise,” a senior Army officer said.

A top Iraqi government official told news agencies Friday that he expects only 100,000 U.S. soldiers and Marines to stay in Iraq by the end of 2006 and a complete withdrawal by 2008.

Despite the administration’s insistence that internal benchmarks will determine if, when and how many troops are pulled out of Iraq, some lawmakers want to force the administration’s hand, while others hope a withdrawal is not precipitous.

Sen. Russ Feingold (D-Wis.) introduced an amendment yesterday that would require the Pentagon to draw up a flexible timeline to redeploy U.S. forces by the end of 2006. 

Responding to a question from radio talk-show host Don Imus about the Pentagon’s plans to withdraw troops, Sen. John McCain (R-Ariz.) said, “I’m nervous about that because I want to make sure the situation on the ground warrants it. … I just hope we don’t pull those troops out too fast for political reasons. I hope the reasons are valid if we do.”

The war in Iraq, however, has been a political issue since House and Senate GOP leaders voted on a resolution giving the president license to use force in Iraq just weeks before the 2002 midterm election. Republicans hammered Democrats who opposed the war, as well as their unwillingness to support relaxing labor rules for employees of a newly created Department of Homeland Security.

As the Iraq war has entered its fourth year and more than 2,300 U.S. troops have been killed and thousands maimed and injured, Republicans are hoping for some good news to change their political fortunes.

Still, the war is a prominent issue in only a few places, such as Connecticut, where Democrat Diane Farrell has hammered her opponent, Rep. Christopher Shays (R) for supporting the war and wealthy businessman Ned Lamont has challenged Sen. Joe Lieberman (D) in the Democratic primary largely because of Lieberman’s support for Bush in the war.

But withdrawing troops won’t directly affect the prospects of congressional Republicans, Winston said.

“It will improve the attitude about the direction of the country and therefore improve the attitude about the people putting those policies in place,” he said.

Not surprisingly, Democrats are skeptical that a major reduction of U.S. forces in Iraq could improve GOP prospects in November.

“Iraq is a big part of people’s discontent and uncertainty,” said Democratic pollster Anna Greenberg of Greenberg Quinlan Rosner. “But so are gas prices, the economy, healthcare costs and retirement security.”

She added that most Americans view Iraq as a mistake. A withdrawal, she said, “would not eradicate any of those feelings of the Iraq war. Just starting to get out does not resolve how people feel about the war.”