The fundamental question about what the United States should do in Iraq is being asked with greater fervor across America and in the nation's capital. The Bush administration is arguing that the nation must stay the course to prevent Iraq from becoming an oil-rich haven for terrorists and to keep the country from spiraling into a bloody civil war that could destabilize the Middle East.

''If they are not stopped, the terrorists will be able to advance their agenda to develop weapons of mass destruction, to destroy Israel, to intimidate Europe, to break our will and blackmail our government into isolation,'' President Bush said earlier this month at Alaska's Elmendorf Air Force Base.

But Bush is fighting waning public confidence in his handling of Iraq and weariness with a war that's claimed more than 2,100 American lives and costs billions of dollars each month.

''I would list all the arguments that you hear against pulling U.S. troops out of Iraq, the horrible things that people say would happen, and then ask: Aren't they happening already? Would a pullout really make things worse? Maybe it would make things better,'' wrote William E. Odom, a retired Army lieutenant general and former Reagan-era National Security Agency director, for a Harvard University Web site.

Odom, now a senior fellow at the conservative Hudson Institute, has called America's invasion of Iraq the greatest strategic disaster in U.S. history.

Nevertheless, national sentiment is shifting toward getting out - but how? More and more options are being debated in Washington, but no single plan prevails. Here's a look at some of the ideas:

Stay the course: This is Bush's approach. He says Iraq is making progress, with a democratic process taking shape and a growing number of Iraqi troops prepared to protect the country.

Last month, 88 Iraqi army and special operations battalions conducted combat operations, according to an October Defense Department report. Of the 88 units, 36 were viewed as being ''in the lead'' or fully independent, a 50 percent increase since July.

''Iraq is making amazing progress from the days of being under the thumb of a brutal dictator,'' Bush said at Elmendorf Air Force Base.

However, Bush says Iraq still needs American protection.

But critics say that the Iraqi forces remain largely Shiite Muslim or Kurdish, with few Sunni Muslims and too many infiltrators from religious militias - and from the insurgency. They also argue that the U.S. military presence in Iraq is the problem, not the solution, because it inflames jihadists and nationalists to attack U.S. troops as a foreign occupier.

''You already have a civil war,'' Odom said. ''As for terror, that's the biggest danger there, but it's already happening. Getting out will allow us to focus on al-Qaida. This war has made it easier for al-Qaida - we still haven't gotten Osama bin Laden.''

Rapid withdrawal: Supporters say it's the best way to stop the killing of U.S. troops, will force Iraqis to take control of their security and future, will prove that the United States doesn't intend to make Iraq its permanent base in the Middle East and thus will lower the passions behind the insurgency and radical jihadists throughout the region.

Rep. John Murtha, a pro-military Democrat from Pennsylvania, caused a stir in Congress recently when he called for the prompt withdrawal of all U.S. troops. Under his plan, troops would begin leaving after Iraq's Dec. 15 election, with total withdrawal within six months. He would deploy a quick-reaction Marine strike force in the region, possibly in Kuwait.

''Our military's done everything that has been asked of them,'' he said. ''The U.S. cannot accomplish anything further in Iraq militarily. It's time to bring the troops home.''

Murtha's opponents argue that a hasty U.S. departure would be like giving terrorist insurgents the keys to the country. It would undercut Iraq's fledgling government before it gets its footing and almost instantly trigger a civil war between Shiite and Sunni Muslims, while ethnic Kurds fight for their own independent state.

A civil war, they warn, could draw in neighboring Iran as an ally to the Shiites; Syria, Saudi Arabia, Jordan and others as allies to the Sunnis; and Turkey as an enemy to Kurds.

Worst-case scenarios see a pro-Iranian Shiite regime in Iraq and Sunni violence spreading to Saudi Arabia, leading to jihadist Muslims ruling the biggest oil producer in the world and spreading instability throughout the Middle East.

It's far better, critics of withdrawal say, to stick with Bush's goal of implanting democracy in Iraq as the first step toward spreading democracy through the region.

Add U.S. troops: This proposal aims to stamp out the insurgency. A plan by Sen. John McCain, R-Ariz., would begin by clearing specific areas of insurgents, using heavy force if necessary, then holding those areas rather than withdrawing. Heavy security, McCain said, would allow reconstruction to proceed without fear of attack and allow civil society to flourish.

Opponents say McCain's idea has little traction with lawmakers heading into next year's midterm elections and little enthusiasm from a military already stretched thin and struggling to meet recruitment quotas.

''More troops, we tried that in Vietnam,'' Odom said. ''It didn't work.''

Gradual withdrawal: This course appears most popular among those seeking a way out of Iraq, especially prominent Democratic senators who may seek the presidency in 2008.

Their ranks include Sens. Russell Feingold of Wisconsin, Joseph Biden of Delaware, John Kerry of Massachusetts, Barack Obama of Illinois and former Sen. John Edwards of North Carolina.

Slow reduction of U.S. forces over the next year or two would allow time to train the Iraqi military to defend its country and help the elected government get itself and the country's damaged infrastructure up and running, supporters say, while reducing U.S. targets there.

Bush and other pullout opponents say gradual withdrawal has the same drawbacks as an immediate pullout and would give insurgents a timetable for planning.

''Pulling out prematurely will betray the Iraqis,'' Bush said in August. ''Withdrawing before the mission is complete would send a signal to those who wonder about the United States' commitment to freedom.''

Such an approach was also tried in Vietnam, where it was called ''Vietnamization.'' It failed because the South Vietnamese government had limited public support, was riddled with corruption and fielded an army that was no match for communist North Vietnam's. Congress cut off U.S. aid to South Vietnam in 1974, which some U.S. conservatives blame for contributing to South Vietnam's fall in 1975.