My reaction to this would be to nuke one of their
cities where we know he isn't being held,
then issue an offical notice:
"If he isn't released, unharmed,
we'll continue to nuke an Iraq city each day.
If he's harmed, we'll nuke them all.
Have a nice day."
I know it's damned tempting in cases like this, but we are the Good Guys, and have to act like it.
The fact is, now that the U.S. is under new management, we are rapidly improving our "non-nuclear options" for dealing with mad dog criminals worldwide. And most of those options are far more unpleasant for their targets than instant vaporization.
If Capt. Speicher is being held in Iraq, those around him know for a fact that they will be held personally accountable for his well-being.
And Allah help them if they kill or mistreat him, because no one else in heaven, hell or on Earth will be willing or able to save them from the wrath of the Delta Force operators, who are expertly trained in extracting both information and vengeance without leaving any tracks.
Given the choice, I'd rather be nuked if I were in their shoes. It's better to die painlessly in a second than slowly and painfully over a period of days, weeks, months or years.