Ever the reluctant warrior, President Obama's sudden display of bold military strength in Iraq this week surprised his harshest foreign policy critics and supporters alike.

As he spoke Thursday about authorizing airstrikes against militants with the Islamic State of Iraq and Syria, Obama was careful to note that he was elected president in part to get the U.S. out of a war with Iraq.

Still, Obama made a compelling case for renewed U.S. leadership in the world in limited and specific cases. The U.S., he said, could no longer "turn a blind eye" to the brutal atrocities against Kurdish minorities and threats to U.S. personnel in the region. And, he argued, because the Iraqi government was asking for America's help, the military action is on firm legal ground.

Obama's more muscular approach to Iraq is designed to be short and targeted, but it will take far more than a few days of airstrikes to stop ISIS and solve the country's complex political and military problems. Here are four reasons the current bombing campaign alone won't be enough.

The intervention will be limited

The White House insists that its airstrikes against ISIS will be targeted and limited, but it could take days, if not weeks, of airstrikes to prevent ISIS militants from posing a continued threat to the region and U.S. personnel in the Kurdish capital of Irbil.

“We are not launching a sustained U.S. campaign against [ISIS] here, because our best way to deal with the threat of [ISIS] over the long term is for the Iraqis to do so,” a senior administration official told reporters Thursday night.

So far, however, the Iraqis have been unable to stop the ISIS advance on their own, and there’s no reason to believe they could without prolonged and robust military support from the U.S.

Arming the Kurds could lead to the break-up of Iraq

The U.S. does not want to arm the Kurdish Peshmerga forces out of fear they will use those supplies later to make a play for independence, beginning the break-up of Iraq. The U.S. has long opposed allowing the Kurds to sell their own oil to buy arms.

So far the U.S. is walking a fine line, trying to limit its support to “training and equipping” the Kurds in a non-lethal manner.

Though the U.S. has pledged not to launch a “sustained” campaign against ISIS, “that does mean that we’re not going to support [the Kurdish and Iraqi forces] in that effort through additional assistance, training, equipping, intelligence and advice,” an administration official told reporters Thursday night.

The U.S. hasn't built a regional coalition yet

Obama hasn’t spent much time or political capital building a “coalition of the willing” — enlisting the support of other countries in the region and trying to reach consensus on a joint plan to fight ISIS.

Such a coalition would be extremely difficult to cobble together, considering it would likely need to find common ground and a common military plan with many staunch enemies, including Turkey, Iran and Saudi Arabia, as well as Syria.

An agreement to fight ISIS in Iraq, a more virulent outgrowth of al Qaeda, could force the U.S. into an allied relationship with Syria’s Bashar Assad regime, a mind-bending turn of events after Obama has spent years calling for regime change in Syria and backed down from launching airstrikes against him last fall after Assad crossed his red line by using chemical weapons against his own people.

The U.S. doesn't have a stake in Iraq's political process

The U.S. has not backed — at least overtly — a candidate to replace Prime Minister Nouri al-Maliki, the Shiite leader largely to blame for creating the political climate for ISIS to seize control of nearly half of the Iraq by disenfranchising the Sunni population.

That leaves the political future of Iraq unpredictable and up for grabs.

The U.S. military intervention this week gives America a more influential position with any new leader, who could be chosen as early as Sunday, and would likely be grateful for U.S. help in keeping the country together during a critical time.

Whether or not that person will be able to hold the fractured regions together over time is an open question.

Grand Ayatollah Sistani, one of the most influential voices in with Iraq’s Shia majority population, has repeatedly called for a prime minister with broad national appeal.

The U.S. is hoping that new leader, inevitably a Shiite, will be able to reassure Sunnis, Kurds and other ethnic and religious minorities that they will have a clear stake in a more inclusive government.

If the leader is strong and inclusive enough, the hope is that Iraqi Sunnis who have either joined forces with ISIS or chose not to fight them as they’ve advanced across Iraq over the last two months may reconsider and turn on them to try to hold the country together.

But changing the balance of power now will be a tall order, after ISIS seized control of Tikrit and Mosul, where it looted $2 billion from banks and became more emboldened about its goal of establishing a borderless caliphate across Syria and Iraq.