In Physics Review Letters (PDF) Neal Lane, Bill Clinton’s second science advisor, offers some sage advice to future advisors:

I believe there are some lessons to be learned—from the experiences of previous Science Advisors—that may provide guidance for the future.

First, presidents must make decisions based on various kinds of often conflicting information— economic, strategic, political, as well as scientific—and they have to weigh that information in setting policy. Science is a special kind of information but, often, not the deciding factor. The value of advice given by a Science Advisor to a President depends on it being objective, based on the best current scientific understanding, and completely confidential. So, if one does not hear the Science Advisor taking a public position that we might consider appropriate but that goes against the Administration’s policies, one must keep in mind that just goes with the job.

Second, the presidents’ Science Advisors (by various titles) are not generally members of the inner circle of political advisors, most of whom are in the White House because of their personal relationships with the President or their political expertise or both. Indeed, only relatively recently, in the Administrations of George H. W. Bush and Bill Clinton, did the Science Advisor have the title Assistant to the President and report directly to him. Having that access to the President, using it judiciously, and not being in the inner circle of political advisors is the ideal situation. Guy Stever has said that it was a good thing that science was not in the White House during the Watergate disaster. I am inclined to agree with him, although I arrived in the White House shortly before the impeachment of President Clinton, and the work of the White House did not come to a halt. Had I been one of the President’s close political
advisors, it would have been difficult to focus on S&T policy.

Third, most of the President’s time is taken up with things that relate to: national security (e.g., the Middle East), jobs and the economy (especially in down times), energy and environment, health and education, negotiations with Congress, political events around the country, scandals, bad press, national disasters (e.g., Katrina) and other crises. Rarely is science central to any of these, at least in the short term. Part of the job of the Science Advisor is to watch for opportunities to make science, mathematics, engineering and technology a significant part of the discussion and, in particular, make the important connections with high priority national needs.

Although there are many other lessons, these three are particularly important to keep in mind when thinking about how or whether science advice will be important to future
presidents.