When Defense Secretary Ash Carter announced yesterday that we were conducting ground operations in Iraq "at the invitation of the Iraqi government", he made it sound like we are cleared this with the government of Baghdad.

Nothing could be further from the truth.

The United States said on Tuesday it was deploying a new force of special operations troops to Iraq to conduct raids against Islamic State there and in neighboring Syria, a ratcheting up of Washington's campaign against the group that was quickly rejected by Iraq's government.
Iraqi Prime Minister Haider al-Abadi said the deployment of such a force was not acceptable without Iraq's approval, raising questions over how closely Washington coordinated the plan with Baghdad.

Prime Minister Adabi clarified it further today by saying, "There is no need for foreign ground combat forces in Iraqi territory."

That sounds pretty clear to me, but in case it wasn't, PM al-Adabi back in September said foreign troops are "out of the question."
How many times must Iraq say "Thanks but no thanks" before Washington gets it?

Prime Minister Adabi is saying it nicely. The Shia militias in Iraq are saying it in a different way.

“We will chase and fight any American force deployed in Iraq,” said Jafaar Hussaini, a spokesman for one of the Shi’ite armed groups, Kata’ib Hezbollah. “Any such American force will become a primary target for our group. We fought them before and we are ready to resume fighting.”

Kata’ib Hezbollah has made bold statements before that didn't amount to anything, but they are also an army of tens of thousands that killed dozens of American soldiers during the occupation, and are now armed with advanced weaponry courtesy of the American taxpayer via Baghdad.
Kata’ib Hezbollah isn't alone.

“All Iraqis look to (the Americans) as occupiers who are not trustworthy,” said Muen al-Kadhimi, a senior aide to the leader of the Badr Organisation.

The Pentagon estimated that these Shia militias are responsible for the deaths of 500 American soldiers during the occupation.
Make no mistake, these Shia militias are wildcards beyond the control of Baghdad.

Abadi, a Shi’ite, came to office just over a year ago backed by both the United States and Iran. He promised to rebuild the fragmented country he inherited from his predecessor, Nuri al-Maliki, who was widely accused of fueling sectarian divisions. Since then, though, even more power has shifted from the government to the militia leaders.
...
One army division is now under informal militia command, according to U.S. and other Western military officers. Shi’ite paramilitary elements have taken at least partial control of the Interior Ministry, according to security officers, Iraqi politicians and U.S. military officials. ...Militia leader Amiri warned in a televised interview last month that if the Shi’ite groups did not approve of U.S. military operations in Iraq, “We can go to Abadi and the government and … pressure them: ‘Either you will do this, or we will do that.’” Amiri did not specify what action his group would take.

Basically Iraqis are done being occupied by American troops, and if we invade again we are going to be getting shot at by more than just ISIS.
Iraqis don't like us for more reasons than just we've killed hundreds of thousands of them and destroyed their country. They also think we are working with ISIS.

On the front lines of the battle against the Islamic State, suspicion of the United States runs deep. Iraqi fighters say they have all seen the videos purportedly showing U.S. helicopters airdropping weapons to the militants, and many claim they have friends and relatives who have witnessed similar instances of collusion.
Ordinary people also have seen the videos, heard the stories and reached the same conclusion — one that might seem absurd to Americans but is widely believed among Iraqis — that the United States is supporting the Islamic State for a variety of pernicious reasons that have to do with asserting U.S. control over Iraq, the wider Middle East and, perhaps, its oil.
...
The Islamic State is “almost finished,” he said. “They are weak. If only America would stop supporting them, we could defeat them in days.”

It seems amazing that once again America has decided that Iraqi opinions and their sovereignty doesn't matter. It's as if we learned absolutely nothing from the last time.
The difference this time is that partisan Democrats have forgotten what they should have learned as well.
What do you think will happen the first time the Shia militias wipe out a platoon of American soldiers? Do you think party loyalty will prevent that from becoming an enormous PR disaster? It'll be Mogadishu all over again.

While we are at it, the Syrian government never gave us permission to deploy soldiers there either. So that's two countries we are invading, without UN approval, without NATO approval, and without an AUMF.