A fined tuned argument.....Heywood style.

[Angrboda]

The argument from fine-tuning is basically just an argument from design in cosmological dress. The article in the IEP linked below on the argument for arguments for God based on design includes many objections based on biological design which apply equally to the fine tuning argument.

Basically, there are two ways to conceive of the fine tuning argument. The first, is as an argument from ignorance. "Not X, therefore Y." An argument from ignorance is fallacious and its conclusion is therefore not justified, so you can't get to God via this route. The other way to conceive of the fine tuning argument is that it is a Bayesian argument of which of the given alternatives is most probable. For this type of argument to succeed, the probabilities of each alternative must be estimated. Perhaps a random universe is improbable, but that means nothing if the probability of a universe designed by God is even lower. However, since nobody can provide any justification for assigning a probability to the alternative of "design by God," this argument can't be completed either. So neither approach to the design / fine tuning argument leads to a successful, justified conclusion that it was designed by God.

There's an additional difficulty, being that, even if we accept that the facts "cry out" for explanation, they only cry out for an explanation of the fine tuning. That God satisfies this need may be one answer, but there may be many others, answers that are unknown, which may satisfy this cry. You need to prove not only that fine tuning demands an answer (it doesn't), but also that the answer which satisfies that cry is what we would call a god. People who argue fine tuning tend not to realize that showing fine tuning is one of the baby steps of the argument. Without the other major steps, you have nothing.

For what it's worth, I've never heard a fact utter a cry yet. Biased observers, yes, facts, no.

The following article from the IEP points out how all design arguments, including fine tuning, fall short.
http://www.iep.utm.edu/design/

The following article on William Dembski's work on intelligent design, while lengthy, demonstrates how big the gap which exists between arguments that claim the need for design "cries out" and what the facts actually do is.
http://www.talkorigins.org/design/faqs/nfl/