The United States does not want to go back to the Iraqi quagmire, which reminds one of the scenes in Godfather part III: ‘Just when I thought I was out they pull me back in.’
Iraq is in the headlines, facing similar troubles it had when US forces were deployed there (2003-2011). The Obama administration might seek to give the Iraqi regime an offer they cannot refuse: saving them from Sunni rebels in return for Iraq carrying out real political reforms that would make that torn country more stable and less a pro-Iranian Shiite dictatorship, as it is now. But the Iraqi government, once the danger from Sunni rebels is over, courtesy of US help, would probably ignore American interests again, as they did supporting Assad in Syria in recent years.
Meanwhile the Obama administration is sending to Iraq up to 300 advisers i.e. Special Forces. In 480 BC a similar number of elite troops, from Sparta, fought in a known battle against the Persians. Now it is a possible option the 300 Americans in Iraq might have to work with the Persians i.e. the Iranians.
The threat to the Iraqi government comes from Sunni groups like the ISIL/ISIS (Islamic State in Iraq and the Levant / Islamic State in Iraq and Syria). This non-state organization wishes to create a huge state starting with two existing ones, Iraq and Syria. The ISIS, the men in black, wear this color like the Nazi SS did. This is another resemblance between those two radical and violent groups as it is expressed in both their ideology and actual approach towards their enemy.
ISIS is the enemy of Iraq, Iran, Israel and western powers like the United States. All those states could not form a coalition because of the disputes and conflict of interests between them, particularly between Israel and Iran.
Israel would not operate alone in Iraq. The last time Israel attacked targets in Iraq was in 1981, in the raid that destroyed Iraq’s nuclear reactor. This by the way served Iran as well since it was fighting against Iraq at the time. Israel almost bombed targets in Iraq in 1991, when Iraq launched long range surface to surface missiles at Israel. In spite of Israel’s concerns about the ISIS it would not, at least not officially, join any fight against the ISIS in Iraq.
Iran and the United States could dance together i.e. collaborate against the ISIS although the two states would remain adversaries. In this case my enemy’s enemy is still the enemy. In the 1990s and 2001 Iran and the United States had joint foes like the Taliban. Yet during the war in Afghanistan Iran has been supporting insurgents who attacked US troops. Iran is therefore a problematic ally, to put it mildly.
There are also the talks between the United States and world powers and Iran about the Iranian nuclear project i.e. the Iranian ambition to have nuclear weapon capability. An agreement on this issue could influence a deal about Iraq and vice versa. It could be bad news for Israel if Iran gets a break in the nuclear issue in return for another American attempt to save Iraq from itself.