Here's a news story on the proposed legislation. Two pieces, count-'em two! Well, one is just a resolution. The other, STOP, stands for the Safeguard Tribal Objects of Patrimony Act. So far as I can tell, the main things the legislation does are two: to double the jailtime it is possible to get on conviction for a second offense, and require the Comptroller General to submit a report estimating number of artifacts trafficked and number of prosecutions, "after collecting information from the Attorney General, the Secretary of the Interior, and the Secretary of State, and meeting, as appropriate, with Indian tribes and Native Hawaiian organizations".
Unfortunately, none of those entities, so far as I know, has the capacity or interest or wherewithal to provide estimates of the extent of the illicit market. As to the doubling of penalties, the theory of deterrence requires that the risk of actually being prosecuted be factored into the deterrent effect. Saddam introduced the death penalty for looting when he lost control, with no discernible impact. So long as the risk of prosecution remains low -- which it will absent some increased incentives to prosecute, increased provision of financial resources to prosecutors, requirements to expand prosecutions, or changes in the burden of proof to make prosecutions cheaper and easier -- there's not likely to be much impact. Nice acronym, though.