(CNN) -- New Jersey Gov. Chris Christie says he had some "pretty good fights" with Sen. Frank Lautenberg. But Lautenberg's death early Monday puts the Republican governor in a pretty good bind in replacing him.
"It's no mystery that Sen. Lautenberg and I didn't always agree," Christie said Monday of the liberal Democrat. "In fact, it probably is more honest to say we very often didn't agree, and we had some pretty good fights between us over time -- battles on philosophy and the role of government."
As Christie, a Republican, runs for what is expected to be a relatively easy re-election, he now invites unwanted attention as he decides on a temporary replacement for Lautenberg.
If he doesn't name a conservative, that could complicate his already strained relationship with conservatives from across the country, which could spell trouble if Christie decides to run for the 2016 GOP presidential nomination.
Two conflicting New Jersey state laws about when to hold a special election to fill a vacant U.S. Senate seat add complexity.
One statute says that "if a vacancy shall happen in the representation of this State in the United States Senate, it shall be filled at the general election next succeeding the happening thereof, unless such vacancy shall happen within 70 days next preceding such election."
The next general election in the Garden State is in November, when Christie is up for re-election. Since Lautenberg's death is not within 70 days of that election, a special election to fill the final year of Lautenberg's term could be held this November.
But another state statute says that if the vacancy happens within 70 days of the primary that precedes the next general election, the special election will be held at the second succeeding election.
The primary for this November's contests is Tuesday. Since Lautenberg's death is well within that window, under this provision an election would not be held until November 2014, with the winner serving a full six-year term.
Both statutes agree that the governor is authorized to set the date for such an election.
There are some obvious political advantages for Christie to put the election off until 2014.
Polls show that Christie has a 2-1 advantage right now over Democratic state Sen. Barbara Buono. But a Republican strategist from New Jersey tells CNN that a special Senate election this November could increase Democratic turnout, especially if Newark Mayor Cory Booker is on the ballot. Booker is considering his own run for Senate in 2014.
Even with a very large lead over Buono, why would a GOP governor running for re-election in a blue state want to invite higher Democratic turnout this year?
If Christie decides to hold the Senate contest in 2014 with a hand-picked replacement serving 18 months by Election Day, it could invite legal action from New Jersey Democrats.
State party Chairman John Wisniewski tells CNN that "it's a slap in the face to New Jersey voters not to have a say in who represents them for a year and a half."
Wisniewski says New Jersey Democrats expect the election to be this November, pointing to what he says is the most recent statute by state lawmakers on the timing of such a vote.
Sources close to the governor say Christie has made no decisions because it's so early in the process. But they expect him to announce a 2014 Senate election rather than a special contest this year.
While there's controversy over the timing of an election, an even bigger question is who would Christie name to immediately fill the seat? And what impact would that pick have on his 2013 re-election run and any possible 2016 bid?
One top name to emerge is state Sen. Joe Kyrillos, a longtime Christie ally who last November lost to the state's other U.S. senator, Democrat Bob Menendez, by 20 percentage points.
Other possibilities include Lt. Gov. Kim Guadagno; state Assemblyman Jon Bramnick, who appears to be gearing up to run for the Senate in 2014; and state lawmaker Tom Kean Jr., son of former GOP Gov. Tom Kean, a political mentor of Christie.
Some pundits have suggested that Christie could even appoint the former governor, now 78, as a caretaker until a special election.
There were also rumors Christie would consider Booker, since the Democrat took a pass on challenging him for governor this year. But both sides shot down such a farfetched scenario.
Christie is touting his ability to work with Democrats, and he's won the endorsement of a number of Democratic politicians.
Choosing a moderate Republican would not rock the boat, but choosing a more conservative or partisan Republican could cause problems.
Such a pick, however, would help Christie mend fences with national conservatives, still upset with his praise of President Barack Obama personally and of the federal response in the wake of Superstorm Sandy.
While Christie's approval rating in New Jersey soared after Sandy and has remained high, some commentators in his own party blasted him for his praise of Obama, saying it contributed to the defeat of GOP nominee Mitt Romney.
Christie's criticism in January of House Republicans' slow -- but eventual -- approval of federal recovery aid to Sandy victims and the governor's teaming up with Obama again last week to promote recovery efforts along the Jersey shore haven't helped.
Rich Bolen, a GOP activist in South Carolina, the first Southern state to vote in the presidential primary and caucus calendar, expressed a critical conservative sentiment.
"Christie burned a lot of bridges with conservatives and tea partiers before the last election cavorting with Obama in the Sandy aftermath. Even though most people don't think it really affected the election, it just made Christie look more wishy-washy," he said.
"If Christie appoints a "Northeast moderate placeholder, red state America will be irrevocably opposed to him throughout the 2016 primary process," added Bolen, the former head of the Lexington County, South Carolina, GOP.
Similar feelings were found in Iowa, which kicks off the overall caucus and primary calendar.
"I do think that Gov. Christie's selection will have a major impact on his 2016 presidential aspirations," said Craig Robinson, a GOP strategist and founder and editor-in-chief of the Iowa Republican.
"Many conservatives have grown frustrated with Christie since last November and this provides him an opportunity to heal some of those wounds by appointing someone who has broad appeal with Republicans. If Christie would happen to nominate a Democrat, any presidential aspirations would immediately go up in smoke," he said.
Christie's quandary was so appetizing, it even invited a comment from David Axelrod, the senior adviser behind Obama's 2008 and 2012 victories.
"Fascinating dilemma for Christie. Does he name interim who reflects his more moderate state, or feed Tea Party for '16?" tweeted Axelrod.