Could Obama be Impeached for Attacking Syria?

If the vote fails in the Congress, it's possible.

In 1973, the Congress enacted the War Powers Resolution. Nixon vetoed it, but his veto was overridden and the bill became law. There are three permitted reasons for a president to order forces into combat: Congress declares war, Congress passes specific authorization, or a national emergency is created by an attack upon the United States, its territories or possessions, or its armed forces.

That's it. There is no statutory authorization for this president (or any other) to open hostilities with another nation because they are alleged to have committed atrocities against their own people. I submit to you, Gentle Reader, that the President has no more authority to do that than the commander of an infantry battalion.

President Obama could have just started the bombing, like President Clinton did in Kosovo, and basically say to Congress "yeah, so what". But he didn't, he chose to ask Congress for authorization to attack Syria.

If he doesn't get congressional authorization to attack and then does so anyway, Congress should vote to impeach him.* Otherwise, we might as well march on the National Archives and burn their original copy of the Constitution.
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* Not that President "Warning Shot" Biden will be any great improvement.