We thought we knew just how many seats Republicans needed to win in order to regain a Senate majority in 2012.

Then came Angus King.

The independent former governor of Maine entered that state’s open Senate race Monday night as the prohibitive early favorite, throwing a wrench in Democrats’ plans to win the seat from Republicans.

Or at least it would seem.

There is considerable thought that, while King would run as an independent, like independent Sens. Joe Lieberman (Conn.) and Bernie Sanders (Vt.), he would caucus with Democrats once he joined the Senate.

And given that the battle for the majority could be close, it’s not unreasonable to think that King could be a King-maker — for somebody — come January 2013.

Maine aside, Republicans could effect control over the Senate if they gain three seats (forcing a tie) and win the presidency.

If King wins and doesn’t caucus with anybody, then there is no prospect of a tie; Republicans win the majority if they gain four seats, while Democrats keep the majority if they lose three or fewer.

If King wins and caucuses with Democrats, that would be as good as a Democratic victory when it comes to deciding the majority, and Republicans would need to win four other seats just to gain a tie.

The problem is, King is keeping his options open right now, which means we won’t know for sure which scenario we’re dealing with.

The idea that King would caucus with Democrats makes sense for a number of reasons.

First, senators need to caucus with a party to earn committee assignments and gain clout in the Senate. Without teaming with a party, King would essentially just be casting votes.

And second, he is considered more of a left-leaning politician and actually worked for a Democratic senator from Maine in his earlier days. King became an independent when he decided to run against Democratic former governor Joseph Brennan in 1994, and his personal wealth has allowed him to run without a major political party infrastructure supporting him.

Republicans have openly speculated that a deal — or at least an understanding — is in place that King will caucus with Democrats.

“This development adds a complicating factor for national Democratic Party strategists and adds fuel to growing rumors we heard from sources on the ground in Maine this weekend that the Democratic Party establishment in Washington is pressuring liberal Democratic Rep. Chellie Pingree to step aside for the Independent former Governor,” Rob Jesmer, the executive director of the National Republican Senatorial Committee, wrote in a memo Monday.

King’s former campaign manager, Kay Rand, told The Fix that caucusing with a party is an option.

“He hasn’t made that decision yet,” Rand said. “Everything is on the table; he’ll do what’s best to advance Maine’s interests.”

Democratic Senatorial Campaign Committee Chairwoman Patty Murray (D-Wash.) told The Hill on Tuesday that she hasn’t spoken with King, and she declined to speculate about whether the DSCC might back him.

In announcing his campaign yesterday, King said he would go to Washington in an effort to shake up both parties.

“If you like the system as it is, I’m not your guy,” King said, according to the Bangor Daily News. “If you want a shot at changing it, join me.”

That kind of rhetoric would mean a little less if he joined the Senate and immediately joined forces with Democrats, but caucusing with a party doesn’t mean you can’t antagonize it frequently (see: Lieberman, Joe).

In other words, even if King wins and does wind up caucusing with Democrats, it’s not an ideal situation for Democrats. And given that King endorsed George W. Bush for president in 2000, the left wing of the party may be screaming for someone more along the lines of a Pingree.

The national Democratic Party has been eerily silent in recent days on the matter, but sources say there doesn’t appear to be a broad effort to collect signatures for Pingree before the fast-approaching March 15 deadline.

Pingree and King are very close friends, and it remains to be seen whether she will press forward with a campaign against him.

Democrats will field a candidate; the question is how strong. If national Democrats push forward trying to get a strong candidate — perhaps former governor John Baldacci — they risk splitting the Democratic vote so much that it allows Republicans to win.

By contrast, if Democrats believe or have some assurance that King will caucus with them, the better call might just be to throw in the towel in an effort to make sure that the Democratic nominee doesn’t steal so many votes that Republicans could win.

Either way, King is the early favorite as a very popular former governor. He took 59 percent in a three-way reelection race in 1998 (that’s not a typo).

As we saw with Florida Gov. Charlie Crist when he switched to become an independent in 2010, there will be pressure throughout the campaign for King to decide which party — if any — he would caucus with.

But King, unlike Crist, is probably strong enough that he can simply defer and not pay too much of a political price.

The most surprising decision, indeed, would be for King to not caucus with either party. That’s an exceedingly rare thing in the Senate.

The last independent to leave the Senate, former Republican Sen. Jim Jeffords (Vt.), caucused with Democrats after leaving the GOP in 2001. Sen. Harry F. Byrd Jr. (I-Va.) also caucused with Democrats after leaving the party in 1970, and Sen. James L. Buckley (N.Y.), who was elected under the Conservative Party banner in 1970, caucused with Republicans. (Interesting tidbit: Buckley was the brother of conservative icon William F. Buckley.)

According to a Fix review, in at least the last 50 years (and likely even longer), only two independent senators have declined to caucus with a party, and neither of them did so for more than a few months. Appointed Sen. Dean Barkley (Minn.) was only in office for a matter of weeks, and Sen. Bob Smith (N.H.) left the GOP in July 1999 as he eyed a presidential bid, but returned to that party in November of that year. He never lost his committee assignments.