Simpson rejected that request on Aug. 15, relying heavily on plans by the Department of State to develop a new form of identification for voters having trouble obtaining other types of state ID.
PennDOT started offering that new voter ID on Aug. 27.
The Supreme Court, which heard an appeal of Simpson's ruling on Thursday, said he is "obliged" to issue a preliminary injunction if he finds that the state is not providing "liberal access" to the new ID cards or if any voter will be unable to cast a ballot because of the voter-ID law.
The order gives Simpson until Oct. 2 to make that call.
Simpson, in his Aug. 15 ruling, estimated that "somewhat more than 1 percent" of registered voters didn't have the necessary state identification to vote as of June. That puts the number of people without the required ID at more than 89,000.
Ron Ruman, spokesman for the Department of State, said Monday that about 9,000 new identification cards have been issued for voting purposes since the legislation was approved by the Republican-controlled Legislature in March.
Tuesday's order was approved by four of six Supreme Court justices - three Republicans and one Democrat. A seventh justice, Republican Jane Orie Melvin, has been suspended by the court while facing criminal charges in Allegheny County. She is accused of using state resources for political campaigns in 2003 and 2009.
Two Democrats on the court, Justices Debra McCloskey Todd and Seamus McCaffery, filed a pair of joint dissenting opinions arguing that the Supreme Court should act now on the request for a preliminary injunction.
Todd noted that the presidential election is just 49 days away.
"The eyes of the nation are upon us, and this Court has chosen to punt rather than to act," Todd wrote. "I will have no part of it."
McCaffery dismissed the urgency of the state to use the law in the general election as "purely political." He pointed out that the state has offered no proof of the in-person voter fraud that the voter-ID law is designed to prevent.
"I cannot in good conscience participate in a decision that so clearly has the effect of allowing politics to trump the solemn oath that I swore to uphold our Constitution," McCaffery wrote. "That Constitution has made the right to vote a right verging on the sacred, and that right should never be trampled by partisan politics."
Contact Chris Brennan at firstname.lastname@example.org or 215-854-5973. Follow him on Twitter @ChrisBrennanDN. Read his blog at PhillyClout.com.