As U.S. troops supported by Iraqi forces continue their assault on Fallujah (search) in an effort to rout terrorist insurgents, questions are swirling about whether the military effort will help or hurt President Bush (search) as he prepares to begin his second term in office.

Military and other experts have said that purging Fallujah of insurgents — many of whom are believed to be responsible for attacks against coalition and Iraqi forces since Saddam Hussein was deposed — is vital to the success of the country's first democratic elections, scheduled for January.

"I think it's important for the world. I don't think it matters for the second Bush administration," said Republican strategist Rich Galen.

"We need to pivot off the day-by-day domestic political attributes of these things … I think it's critical to understand that the confidence that the Iraqis are showing in Prime Minister [Ayad] Allawi (search), in terms of directing these activities, is extraordinarily important as we move toward the Jan. 27 or 29 elections," Galen said.

But others say the Fallujah assault is the Bush administration's chance to make up for "miscalculations" made in Iraq.

"I think we're all more worried about the danger that's facing our men and women over in Iraq right now than the political dangers," said Democratic strategist Rich Masters.

But, Masters added, the administration missed a chance when some military commanders, like former Army Chief of Staff Eric Shinseki, warned before the war that more U.S. troops would be needed to secure the peace than entered Iraq last year.

"I think it points back to probably a miscalculation that the Bush administration made last year ... so now we're paying the price for not listening to military leaders," Masters said. "Let's hope the battle goes quickly … it's definitely critical if we want the elections to go forward in a peaceful manner come January."

The general school of thought is that insurgent activity will increase as Iraq moves closer toward holding free elections. Thousands of terrorists have been holed up in Fallujah for months and finally, Allawi gave the U.S.-led coalition the green light to clear the city of any terror groups that may be thwarting progress in the country.

The Bush administration, meanwhile, has been steadfast in maintaining that Iraq will hold scheduled elections in January and they will not be postponed. Keeping the timetable, like the handover of government authority last June, is considered a psychological achievement as much as a step toward democracy in the nation.

The president himself has been monitoring developments in Fallujah and other terror hotbeds.

"At the request of the Allawi government and alongside of Iraqi troops, coalition forces are now moving into Fallujah to bring to justice those who are willing to kill the innocent and those who are trying to terrorize the Iraqi people and our coalition, those who want to stop democracy," Bush said Tuesday while visiting wounded soldiers at Walter Reed Army Medical Center. "And they're not going to succeed. "

Secretary of State Colin Powell said Tuesday that if terrorists were allowed to operate in Fallujah, they would be "essentially denying the Iraqi people the opportunity to participate in the political process which is now underway leading to elections at the end of January 2005.

"And so, Iraqi forces, alongside coalition forces, have assaulted Fallujah for the purpose of putting down this insurrection, [and] putting down this insurgency and reasserting control," Powell said.

Defense Secretary Donald Rumsfeld on Monday told reporters he couldn't say whether the current siege on the city represented the last big hurrah on the part of the U.S. military to get rid of terrorists there. But U.S. officials have insisted they'll continue the effort for as long as it takes.

"Frankly, as long as we've disrupted the insurgents, we've made it harder for them to plan, to rest, to accumulate weapons, to attack innocent Iraqis and disrupt potentially the election in January, that is the key to success," said Sen. John Cornyn, R-Texas. "We're absolutely determined to support the Iraqi people and finish the job we started."

"People said it was impossible for us to turn the reins back to the Iraqi people. Of course we did … [they] said it was impossible to get into Baghdad in 23 days" when the war began, Galen added. "We did that."

P.J. Crowley, who served as special assistant to former President Clinton for national security affairs, said terror operations in Iraq need to be thwarted enough so that the coalition gains "the upper hand" and can secure the elections.

"We're left to do some heavy lifting" in the days before the election, Crowley said, adding that the Bush administration already "squandered" 600 days in which more work could have been done to secure the country.

"We have to conduct an election," Crowley continued. "There's a lot of work to be done and unfortunately, because we've taken so long to do this, we're now having the policy equivalent of having a Hail Mary pass in the fourth quarter."

But others say the fact that Bush was re-elected last week goes to show that the United States is at least somewhat satisfied with Bush's ability to make decisions where Iraq is concerned and that many Americans believe the country is going down the right road.

"I think the political questions surrounding the whole Iraq security questions were answered with a lot of clarity and in a resounding way in the elections," said Ed Rogers, who is a former aide to President George H.W. Bush. "And the American people have demonstrated their trust in what the president is trying to do there. I do think the situation in Fallujah does need to be better. By any standard, the insurgents are making sort of a last organized stand there. And so, yeah, it's important it go well."

Meanwhile, Al Qaeda-linked terrorists Abu Musab al-Zarqawi (search) and ringleader Usama bin Laden (search) are still at large; Zarqawi supporters have claimed responsibility for a myriad terror attacks and beheadings in Iraq. Even though the presidential campaign is over in the United States, the at-large status of these two terrorists could dog the administration.

"I think al-Zarqawi does remain an issue," Masters said. "I don't think capturing any one man necessarily puts an end to it … Zarqawi is clearly a key to peace in both that region and throughout the rest of the country.

"I think it is critical from a psychological standpoint, for the morale of our troops, morale of our country, that both al-Zarqawi and bin Laden are brought to justice and behind bars. I think it would give both the United States, as well as our troops on the ground there, a clear moral victory and really help us kind of get through this tough time."