We've discussed this quite a bit over the last few years. I don't think a SCOTUS ethics code is a horrible idea, but it's not clear to me that it will make things better, add legitimacy to the court, etc. (They already acknowledge that they consult with the existing judicial ethics code.) And it definitely was a partisan push from the left reaching a crescendo before the decision on healthcare reform.
Now the issue gets raised in the context of the political activities of Clarence Thomas's spouse. (In response to that, consider Judge Reinhardt's opinion on why he didn't recuse himself for his wife's activities in the same sex marriage cases.) Admittedly, just because the push was partisan it doesn't mean that the idea itself is flawed.
Here's the first paragraph from the Geyh-Gillers article:
A code of ethics binds nearly every judge in America. The sole exceptions are the justices of the Supreme Court. Today, for example, no ethics rule prevents a justice from engaging in political activity, speaking at the fundraising event of a partisan organization, or joining a club that discriminates based on race, sex, religion, or national origin. Ethics rules for all other federal judges forbid these activities. This vacuum is unacceptable.