We are in a strategic pause as the White House and the world try to assess the impact of the Iraq war.

The Bush administration is clearly hoping there will be a “demonstration effect” from the fate of Saddam’s regime. Rhetorical slaps at Syria and Iran are testing whether other rogue states will bend without the need for more wars.

I think the “demonstration effect” will depend heavily on what happens inside Iraq in the coming months.

President Bush has gone out on a very public limb with his pledge to make Iraq a model for the region. That pledge puts U.S. credibility on the line. If Iraq remains chaotic, the “demonstration effect” will falter. But internal Iraqi politics are proving much more complex than the Pentagon expected.

The most dramatic example is the assassination of a prominent Shiite Muslim moderate, Abdul Majid al-Khoei, on whom U.S. officials were counting to mediate between them and leading Shiite clergy. Another sign: as U.S. officials convened the first meeting of future Iraqi leaders in the southern Iraqi town of Nasiriyah, thousands demonstrated nearby with signs reading “No to America and Saddam.”

Such signals point to three factors the administration may have originally underestimated in its plans for The Day After. Each has the potential to undercut White House plans for Iraq.

“The Shia Factor. U.S. officials downplayed the role that religion was likely to play in Iraqi politics. But decades of repression by Saddam’s regime increased religiosity among Iraqi Shiites, who make up 60 percent of Iraq’s population. With the collapse of the Baathists, some clerics may try to assert claims to power.

The murder of al-Khoei lay bare the potential competition between clerics. Al-Khoei, son of the late and pre-eminent Grand Ayatollah Abul-Qasim al-Khoei, believed in a separation of mosque and state and supported the Americans. His alleged assassin, the son of a cleric killed by Saddam in 1999, was reputedly anti-Western.

The religious player likely to gain the most from al-Khoei’s death is a Tehran-based Iraqi exile, Ayatollah Mohammed Bakr al-Hakim, who heads the best-organized Shiite opposition group, the Supreme Council for Islamic Revolution in Iraq. He told me in Tehran in February that sharia – the Islamic legal code – should be one of the sources of law in Iraq.

U.S. officials had been courting Bakr al-Hakim, whose brother met with Dick Cheney. But lately, the Pentagon started cold-shouldering him out of fear he was too close to Iran. He has reciprocated by condemning the U.S. presence in Iraq.

The bottom line: Internal Shiite politics in Iraq may be brutal and messy, and with al-Khoei’s death there is no obvious moderate for the Americans to count on. If they alienate clerics who are suspicious about the U.S. presence, U.S. forces might soon face suicide bombers.

“The Iran factor. If the United States continues to treat Tehran as part of the axis of evil, Iranian officials have incentive to stir up anti-American activity among Iraqi Shiites. Some speculate that Iran, perhaps through Bakr al-Hakim, may have played a role in al-Khoei’s murder – or the demos in Nasiriyah. Iran shares a very long border with Iraq and has many agents within the country.

“The legitimacy factor. No sooner is Saddam gone than it is becoming fashionable for would-be Iraqi leaders to distance themselves from the United States. Neither Ahmad Chalabi, the Pentagon favorite, nor Bakr al-Hakim, attended the meeting in Nasiriyah.

It’s already becoming clear that for any putative leader to have legitimacy at home and in the region he must avoid the label “American puppet.”

This issue of legitimacy is the key reason why it is so important that the United Nations be tapped to convene a Baghdad conference that will select Iraq’s interim government. Of course, the United States would be the key player in the background.

The White House can ignore these three key factors, but at its peril. I suspect the Bush administration will appreciate their importance before very long.

Trudy Rubin is a columnist and editorial-board member for the Philadelphia Inquirer.