DALLAS (CBS.MW) - Four years after leaving Halliburton to become vice president of the United States, Dick Cheney continues to be dogged by controversies surrounding his former company.

But it remains to be seen whether Cheney will be a help or a hindrance to President Bush's re-election effort.

A NBC/Wall Street Journal poll released last week showed that only 10 percent of respondents said they would be more likely to vote for Bush with Cheney as running mate vs. 23 percent who felt that way in 2000. By contrast, 25 percent said they would be less likely to vote for Bush because of Cheney, up from 12 percent in 2000.

About two-thirds said Cheney's presence made no difference in how they'd vote.

"People don't vote for the vice president," said Larry Sabato, director of the Center for Politics at the University of Virginia. "They rarely pay attention to what he has done, is doing, or will do. Halliburton has a relatively low name ID in the public as a whole, and even some of those who have heard of it, can't tell you what they do or the connection to Cheney."

Cheney ran Halliburton HAL, -0.16% from 1995 to 2000. Prior to that, Cheney had been in public service most of his adult life, including serving as defense secretary under President George H.W. Bush, White House chief of staff under President Ford and as a six-term congressman from Wyoming.

David Sirota, a spokesman for the American Progress Action Fund, takes the completely opposite view.

"The fact is that Halliburton has become a symbol for all the waste, fraud and abuse that has been seen in the Iraqi reconstruction," Sirota said. "It's not really about Cheney. It's the fact that Cheney, Halliburton and the connection essentially epitomizes who is calling the shots in the whole administration. The administration takes its orders from large, wealthy, powerful companies."

Cheney, who takes the stage Wednesday night in New York to highlight the president's record and his plans to ensure safety at home, became a target of criticism early on after being accused of favoring Big Oil while crafting the administration's energy policy.

But some energy analysts question if having Cheney as vice president has translated into any real benefits for the oil industry.

"He's done nothing for Big Oil, nothing that I can see," said Jim Wicklund, managing director of energy research at Banc of America Securities. "The oil industry does not consider Dick Cheney their representative. He was a politician in exile when he ran Halliburton, he didn't grow up in the oil business."

Wicklund noted that Halliburton did not have the LOGCAP contract -- a key military contract to help plan for the use of civilian contractors during wartime -- for a period of time during Cheney's stint as CEO. "He said the Defense Department was horrible to work for," Wicklund said.

Halliburton's KBR unit, the engineering and construction arm of the company, was awarded the most recent LOGCAP contract by the U.S. Army in 2001. KBR has been accused of overcharging the U.S. government for oil and food services in Iraq and Kuwait. See latest story.

"We have to focus on the job at hand, not the politics," said Wendy Hall, a Halliburton spokeswoman. "However, the environment in which we find ourselves today has brought an unprecedented amount of scrutiny to the company, and the facts have taken a backseat to opinions and agendas. The facts show that Halliburton has served American troops for more than 60 years, for both Democratic and Republican administrations."

Opponents have also tried to personally connect Cheney to the award of the no-bid Restore Iraqi Oil contract to Halliburton, but no evidence has been offered.

There are also ongoing federal investigations on allegations about things Halliburton did while Cheney was in charge.

Halliburton's Nigerian joint venture is the focus of a formal Securities and Exchange Commission investigation over possibly illegal payments related to a liquefied natural gas facility in Nigeria, the company said in June. It recently agreed to pay a $7.5 million penalty to the SEC for failing to disclose a change in its accounting for cost overruns. Cheney was not charged in that investigation.

The company has also been roundly criticized for doing business in countries with active terrorist groups, including Iran, Libya and Iraq.

"It's almost all politics," Sabato said. "Has Halliburton made some mistakes in Iraq? Maybe. But Cheney doesn't run the company, so who cares?"

Cheney's big problem is that he doesn't help Bush, Sabato said.

"He's not the most popular vice president we've had, but he hurts Bush by omission and not by commission," Sabato said. "He doesn't bring anything to the Electoral College table. Tom Ridge could bring Pennsylvania, or Rudy Giuliani could bring New York. But Wyoming would vote for a comatose Republican."