It has already been offed. From The Congressional Record Feb 27, 2012:

As the costs of publishing continue to be driven down by new technology, we will continue to see a growth in open access publishers. This new and innovative model appears to be the wave of the future. The transition must be collaborative, and must respect copyright law and the principles of open access. The American people deserve to have access to research for which they have paid. This conversation needs to continue and we have come to the conclusion that the Research Works Act has exhausted the useful role it can play in the debate. As such, we want Americans concerned about access to research and other participants in this debate to know we will not be taking legislative action on H.R. 3699 , the Research Works Act. We do intend to remain involved in efforts to examine and study the protection of intellectual property rights and open access to publicly funded research.