The key phrase is "active plot". If they've been involved in plots, as Awlaki was, why wouldn't we assume they were going to be involved in more plots? If they were calling themselves "Regional Commander" of Al Qaeda and calling for others to join in armed attacks on Americans...what other evidence do we need?
You seem to miss that if you join an organization that is party to hostilities against the US, you have lost your citizenship....that is in the US code. It isn't subject to a court proceeding, the state department alone can revoke your citizenship, as it did with a number of US citizens who joined the German army in WWII.
Due process stops at the water's edge. You do not have constitutional rights when you are engaged in combat against the US from a foreign country.
Middleview, I assume you could come up with a list of requirements you think would be sufficient to justify a drone strike, outside a war-zone, to kill a suspect. I could, to. There would need to be probable cause to believe the person was actively plotting to kill Americans, there'd need to be a reasonable basis on which to think that he couldn't realistically be captured alive and brought to trial, and there'd have to be a reasonable belief that he could be killed without excessive loss of innocent lives. Sound good to you? The problem is that each of those three prongs involve a judgment call.
That's not, of course, unusual, in the context of other dangerous people, like suspected murderers domestically. But the way we deal with it is to have checks and balances, so that it's not all in one person's absolute (and secret) discretion to make those calls. For example, for a search to be conducted of a murder suspect's house, both the police and the judge need to concur, in their INDEPENDENT JUDGMENT, that there's probable cause. And in the case of the judge, he's expected to be impartial, not an advocate of a particular side. Moreover, he's expected to be operating within the confines of precedent, and ultimately his exercises of discretion can be reviewed at trial, and upon appeal. That holds people in check. Right now we don't have that with these summary executions. It's entirely within the president's discretion, using only whatever advice and standards he, personally, wants to follow.
I could support a system that allowed targeted killings, if there were standards that had the force of law, and checks and balances that reined in any individual's exercise of discretion. That's not what we have right now.