A three-judge appellate panel sided with Christie and rejected the plaintiffs' arguments in a ruling issued Thursday.
Schaffer hopes for a reversal at the state's top court - which has often sided with Democrats in questions on elections. The court helped Lautenberg return to the Senate when it allowed Democrats to put him on the ballot as a replacement candidate in 2002, even though it was past the state's deadline for a switch.
"We're excited to have another court take a look at it. We think the Appellate Division got it wrong," Schaffer said.
Since Lautenberg's June 3 death, both parties have parsed a muddled state statute that sets the procedures for filling a Senate vacancy. The appellate court ruling in part discussed how the placement of a comma affected the reading of the law.
The Supreme Court's interpretation could affect Christie's bid for a reelection landslide.
Democrats had hoped that having a star Senate candidate - perhaps Newark Mayor Cory Booker - on the ballot in November would boost the party's energy and turnout and help them hold the Legislature.
By choosing to call the election on Oct. 16, Christie set up a Senate primary and special election date that could consume Democrats' energy and attention and campaign cash weeks before he appears on the ballot. The Senate race could shove the gubernatorial contest into the background, hurting the underdog Democratic challenger Barbara Buono's chances of making up ground.
Schaffer's suit, which is not formally backed by the Democrats' state organization, argues that holding the special election just three weeks before the general election will lead to confusion and logistical problems, result in low voter turnout, and add $12 million in unnecessary costs for staging a separate election.
The Appellate Division said Christie "without question" is authorized to call a special election given the law and the timing of Lautenberg's death. The court further said that it is not authorized to rule on the wisdom of the policy and the costs, leaving that to the other branches of government.
But Schaffer said she now can respond to the appellate court's reasoning and to the arguments made by the Christie administration.
Christie's office on Friday reiterated its belief that the governor acted properly.
"Gov. Christie followed the law as established by the legislature and ensured New Jersey voters would have a voice and a choice - in both a primary and general election - in selecting the next U.S. senator for New Jersey," a spokesman wrote in an e-mail. "That's what the law provides and the way it should be."
The plaintiffs suing to move the election day have until 10 a.m. Monday to submit briefs. Christie's office has until 10 a.m. Tuesday to respond.
Contact Jonathan Tamari at firstname.lastname@example.org or follow on Twitter @JonathanTamari. Read his blog 'Capitol Inq' at www.inquirer.com/CapitolInq.