When it merely asks agencies to comply.
Traditionally, presidents have operated on the assumption that they have direct control, via Executive Orders, over the activities of Executive Branch agencies, but not "independent" regulatory agencies established by Congress outside the Executive Branch of government. A few years ago, Bob Hahn and Cass Sunstein, the later of whom is currently head of the Office or Information Regulatory Affairs in President Obama's Office of Management and Budget, wrote a paper (published in 2002 in the Pennsylvania Law Review) in which they argued that the President's could, by Executive Order, bind independent as well as Executive Branch agencies. Today, Mr. Sunstein took a step in the direction of testing that argument, when the OMB published Executive Order No. 13579 on "Regulatory and Independent Regulatory Agencies."
EO 13579 orders that independent agencies should promote the goal of producing a regulatory system that protects "public health, welfare, safety, and our environment while promoting economic growth, innovation, competitiveness, and job creation." The quoted language is from EO 13,563, which the OMB applied to Executive Branch agencies earlier this year. The new EO says that independent agencies should comply with the requirements of that earlier EO "to the extent permitted by law," and should produce a plan to do so within 120 days.
As a matter of principle, I support efforts to improve regulatory (and de-regulatory) decision making. But the new EO raises important interpretive questions, which, depending on how they are settled, could generate constitutional issues for judicial review.
Using words like "should" suggests that the White House is urging, but not requiring, the cooperation of independent agencies. On the other hand, an EO is by definition an "order." So, the question is, does the EO really impose obligations on independent agencies? The only way we'll find out, I suppose, is if one or more independent agencies declines to do what the new EO says they should do. If that happens, and the OMB tries to enforce the provisions against them, a constitutional separation-of-powers issue would arise for the courts to resolve.
UPDATE: Michael Livermore sent me the President's cover letter accompanying EO 13759, which would clarifies that the EO is not, in fact, obligatory on independent agencies. After noting what Executive Branch agencies are "required" to do, the President goes on to write: "With full respect for the independence of your agencies, I am asking you today to join in this review and produce your own plans to reassess and streamline regulations" (emphasis added). Apparently, then, the new Executive Order is not an order at all, but a request, which seems a very odd use for an EO. Why didn't the President choose instead to issue less formal memorandum agency heads? My best guess (and it is only a guess), based on Hahn and Sunstein's 2002 article, is that this is a first tentative step toward a bolder assertion of presidential authority over independent regulatory agencies.