It seems- at least from this account of recent FTC action-the likelihood of groups of physicians banding together to successfully negotiate with third party payers, is either very low or non existent. This is because the FTC considers such action on the part of docs as violating the antitrust laws.
Here is the FTC news release outlining the complaint against a number of groups that represent a large number of physicians in the Chicago area. Appeal of the FTC ruling seems to be an often futile exercise in paying large fees to attorneys with little likelihood of success and very real legal risk. A listing of the large number of physicians who have felt the impact of FTC actions can be found at this site, which also describes the continuing legal battle of one group, North Texas specialty Physicians,whose case is to be heard by the Fifth Circuit Court. Physicians alarmed by the stance of the FTC will not be surprised that both unions and hospitals are apparently exempt from antitrust laws. For a discussion of how the FTC manages instances of alleged "horizontal price fixing" by physician groups from a libertarian, Austrian Economic School point of view go here.
As long as the "negotiation" between third party payers and individual doctors is of the type "here is our offer (based on CMS Medicare numbers),take it or leave it" we have de-facto price controls. Price controls tend to have four consequences: increased demand, decreased supply, poorer quality,and the emergence of a black market. It seems to me that in the medical world of the U.S. we are seeing all but the fourth. See Scalpel for some cogent comments about quality and price controls in medicine.
As long as insurers set the prices for medical services and the FTC prohibits physician groups from negotiating for fees, efforts by physicians to support and take part in P4P programs in the hope that the downward spiral of fees for primary care will be halted will be less effective than rearranging deck chairs on a sinking ship.