Julio Cortez/AP Photo

ABC News' Josh Margolin and Shushannah Walshe report:

New Jersey Gov. Chris Christie is holding a 1:30 p.m. press conference and and sources briefed on the governor's thinking say it's likely he will address the special election process to replace the late Sen. Frank Lautenberg and the dates it's likely to be held.

The governor is not expected to name a replacement resulting from Lautenberg's death Monday.

Even as the scheduled time for Christie's announcement approaches, one person briefed on the discussions said the debate inside the top echelons of Christie's political world were continuing.

"This is happening so quickly," the source told ABC News. "But where they'll end up at 1:30, I don't know definitely. It's not done yet."

The governor and key aides were leaning in last few hours toward an expedited schedule of holding a primary on Aug. 13 and a special general election on Oct. 13.

"But that's going to cost $25 million," the source said, citing state estimates that each statewide election costs $12 million.

Also, paper military ballots must be sent by Aug. 28, according to federal law, making it incredibly tight if a primary is contested. And the New Jersey county clerks who run elections and are a politically potent force on their own are expected to object on the grounds that the special October election must be rejected by the courts because it is "not administratively feasible" with the already scheduled Nov. 5 general election only days afterward.

No matter what Christie announces this afternoon it's likely this will end up in court because of the vague laws surrounding the date Christie can choose for the special election.

"Don't be surprised if to see this end up in the courts," former New Jersey Republican chairman Tom Wilson told ABC News. "There's more than a U.S. Senate seat in play here. There are ramifications for the gubernatorial election. With the statues unclear, expect a legal, political battle royale to play out in the courts."

New Jersey Democratic Chairman John Wisniewski also said the process of filling Lautenberg's seat is murky.

"The statutes are less than clear or at least they are conflicting in one respect," Wisniewski told ABC News. "Since the appointment power rests with the governor, it will remain to be seen how we will respond. Our view is the more recent enactment calls for an election right now and that's the most recent pronouncement of legislative intent, so that should be the statute that should control. But there is another, older statute that is at odds with it in terms of timing."

Names being floated for an immediate appointment include New Jersey state Senate GOP leader Tom Kean Jr., son of the popular former governor who lost to Sen. Bob Menendez in 2006. There's also state Sen. Joseph Kyrillos, former state GOP chairman who chaired Christie's 2009 campaign and lost to Menendez last year. Other potential appointees include Christie's Lt. Gov. Kim Guadagno, Assembly GOP leader Jon Bramnick, and Bill Baroni named by Christie in 2010 to serve as the deputy executive director of the Port Authority of New York and New Jersey. Another name on lists as a placeholder: Tom Kean Sr, Christie's political mentor.