[This post has been updated. It started as a post wondering why there would be no additional briefing in Citizens United. But SCOTUSBlog now reports that there will be additional briefing.]
There will be additional briefing in Citizens United ordered by the Court. According to SCOTUSBlog, “both sides are to file their opening briefs simultaneously by July 24, with amici briefs due by July 31. Reply briefs are due by Aug. 19.” I do not know if supplemental amicus briefs will be accepted.
In my ABA Preview of the oral argument in Citizens United, In noted the following about the government’s response to CU’s argument that Austin should be overruled (which was one of many arguments advanced by CU):

The FEC’s main argument against these points is that they were not properly presented below. As to the Austin argument, the FEC notes that Citizens United did not raise this point below, and that it expressly withdrew any facial challenges before the district court issued its summary judgment. On the merits, the FEC argues that Citizens United presented no special reasons to overcome stare decisis in this case.

The government’s argument about overruling Austin were brief—just a few pages. CU did not present much more. So it makes sense the Court has ordered additional briefing, but it is interesting that the Court did not ask for additional briefing in its order on the question whether the issue is properly presented. Reaching an issue that was not raised in the trial court is unusual for a court that says it is trying to avoid deciding constitutional questions.
FURTHER UPDATE: Amicus briefs will be allowed. Here is the full order of the Court:

08-205 CITIZENS UNITED V. FEDERAL ELECTION COMMISSION
This case is restored to the calendar for reargument. The parties are directed to file supplemental briefs addressing the following question: For the proper disposition of this case, should the Court overrule either or both Austin v. Michigan Chamber of Commerce, 494 U.S. 652 (1990), and the part of McConnell v. Federal Election Comm’n, 540 U.S. 93 (2003), which addresses the facial validity of Section 203 of the Bipartisan Campaign Reform Act of 2002, 2 U.S.C. s441b? The briefs, not to exceed 6,000 words, are to be filed simultaneously with the Clerk and served upon opposing counsel on or before 2 p.m., Friday, July 24, 2009. Amicus briefs, not to exceed 4,500 words, may be filed with the Clerk and served upon counsel to the parties by 2 p.m., Friday, July 31, 2009. Reply briefs, not to exceed 3,000 words, may be filed with the Clerk and served upon opposing counsel on or before 2 p.m., Wednesday, August 19, 2009. The case is set for oral argument at 10 a.m., Wednesday, September 9, 2009.