Unless the regulations changed recently, you're totally safe from the draft if you're not resident here. Which you obviously aren't. Russian citizens who are not residents of Russia (i.e. are not registered as having a permanent address in the country, the famous propiska) are not subject to the military service.

You should check with the consulate but my educated guess is, as far as they're concerned, you're still a Russian citizen but resident in the US. Which means you should be able to get a Russian passport of the kind we use to travel internationally but not the other one, the one which serves as the primary ID inside the country. The only downside of your not having a propiska is you technically have to register with the police should you want to spend more than 90 days in any single Russian city. Oh, and should you want to vote, you should do it where you're resident, i.e. at your consulate in the US (Houston?).

I know all of this because a couple friends of mine used this to dodge the draft back in the 90's, officially renouncing their residency here, with their domestic IDs and propiskas and pretending to move abroad where their fathers were posted at consulates or some such.

As I said, check if the regulations changed but I very much doubt this. Drafting overseas Russians would be unenforceable and the general trend so far has been to relax the draft for everyone, not the other way round. Oh, and to physically draft a Russian citizen they need to take away his domestic ID which you, as a non-resident, can not have in the first place.

Hope it helps