weird metaphor

Makes no sense to me (British English native speaker)

Could be the Americans have 'got it covered', like a rug? But that doesn't really make sense given the context.

I've never heard it before, and I have no idea what it is supposed to mean.

Likewise makes no sense to me. All I can think of is, um, carpet bombing...

My assumption is the same as #2's, that the official means "we have this matter completely covered." I agree that the way the article is written, however, leaves a great deal of room for doubt / misinterpretation, although the version in the NYT is preceded by the phrase "even as they {the Americans} help shepherd the process," which makes the reading more plausible.

(The exact phrase "on this like a rug" yields only one other hit, and in that one it clearly does mean "We have it covered." "Covered like a rug" yields a couple dozen hits with the same implication, but this is not a set idiom in American English or, AFAIK, any other variety of English.)

That was my first thought too -- that they have it covered, but it doesn't make sense if they say it's up to the Iraqis. I just googled and all the hits but one referred back to this NYTimes article. The one other hit referred to some legal business with Starbucks.

I think this is probably an instance of a journalist wanting to use a "colorful" quotation, but neglecting to provide the full context so that it could readily be understood by his readers. Poor editing job by the NYT. Boo.

There is a saying "lie like a rug" which is a pun on the two meanings of "lie." It means to tell untruths blatantly and shamelessly.

On the other hand, I did find
"The media has Kosovo covered like a rug" in a novel published in 2000.
"Duke was covered like a rug." A 1991 novel about football. Matt wants to throw the ball to Duke, but there are too many defensive players around Duke "covering him."
"cover > got you covered [like a rug] Rw (drückt aus, daß man sich um alles kümmern wird)" A 1991 book on "American slang: amerikanisch-deutsch". I can't get the full quote.

And, once I got into Google Groups, I found basketball & football references.
Why do they continually try to pass to a man that is covered like a rug by one or more people.
Then on the intercption play, every receiver on the field was covered like a rug
(Got em') covered like a rug on your floor; Really close, tight defense.

So, I'm guessing sports.

I just googled and all the hits but one referred back to this NYTimes article.

That's odd. I didn't bother with the regular Google search, because I figured you had it, er, covered like rug. But when I went back, I got 14,600 hits for "covered like a rug."

Throwing out things such as "a church lawn covered like a rug with [mushrooms]," I still got lots of sports hits. But I also found

Rachel Maddow has this issue covered like a rug.
From thoughtful observations to bathroom humor, Silverstein has childhood covered like a rug [in his autobiography]
Whether it's a nuclear first-strike against the neighbors or an orbital Death Ray with all of the trimmings, Narbonic [a comic strip] has weapons of mass destruction covered like a rug.