The first order of business for freshly sworn-in Virginia state senators is a snooze of a resolution, one that sets out how many seats Republicans and Democrats get on each committee.

It’s important stuff — committees control which bills reach the Senate floor for a vote, and which ones die — but it’s also a foregone conclusion. After all, everyone has known since Election Day which party will rule the Senate.

But not this year.

Two months after elections left the Senate with 20 Republicans and 20 Democrats, the General Assembly convenes Wednesday with the parties still fighting over who will control Richmond’s upper chamber.

The GOP, which already had the House and governor’s mansion, says it will be in charge because Lt. Gov. Bill Bolling, a Republican, breaks tie votes. The Democrats contend that Bolling cannot vote on Senate organization — including committee makeup — and that power must be shared.

So the sleepy procedural votes that normally kick off the Senate’s opening day promise to become a fierce battle, one likely to be fought with arcane parliamentary maneuvers and a second run at a lawsuit. Each party says the other has been trolling for turncoats, offering plum committee posts to those willing to cross party lines. (Both parties deny doing any such thing.)

“We’re in uncharted waters,” said Sen. Janet D. Howell (D-Fairfax). “The stakes are extremely high and I don’t think the public wants a Republican power grab.”

While Democrats characterize Republicans as power-hungry — Sen. A. Donald McEachin (D-Richmond) last week compared Bolling to Alexander Haig, President Reagan’s famously assertive secretary of state — the GOP describes Democrats as in denial.

“The bottom line is, we have to organize and go forward,” said Sen. John C. Watkins (R-Chesterfield). “And if they want to be obstructionist, that’s entirely up to them.”

How Democrats intend to fight a GOP takeover remains uncertain. The Democratic Senate Caucus plans to meet at a Richmond hotel on Sunday to strategize.

Some Republicans have it that Democrats will flee the commonwealth to deny Republicans a quorum. Democrats say they’ve ruled out flight. More likely: elaborate procedural maneuvers aimed at blocking certain Bolling votes. If that doesn’t work, they’ll probably head to court.

“We will react accordingly,” said McEachin, noting his pending lawsuit against Bolling.

The case, filed in December in Richmond Circuit Court, has so far gotten McEachin nothing but mocking. “Democrat Sore Loser Suit,” the GOP calls it. Judge Beverly W. Snukals declined to issue the temporary injunction McEachin sought to block Bolling from voting on organization, ruling that the issue was not “ripe” because he had not yet cast such a vote.

Yet Snukals has not dismissed the suit, which seeks a declaration that the lieutenant governor cannot vote on certain matters. McEachin hinted that he’ll seek another injunction if Bolling votes on organization.

But there’s a catch: Under state law, the lieutenant governor, like the governor and General Assembly members, cannot be compelled to appear in a civil court matter during the session, nor for 15 days before or afterward. If Bolling refused to appear, McEachin’s case could not be heard until after session.

So even if the Democrat prevailed in court, it would be hard for the judge, who raised separation-of-powers concerns when denying the injunction request, to find a good post-session remedy, said A.E. Dick Howard, a constitutional law expert at the University of Virginia.

“Courts are disinclined to take action where it would invalidate an entire legislative session,” he said. “I can’t think of any precedent for that.”

But an after-the-fact court victory could, Howard said, bring about power-sharing for the remaining three years of the Senate term.

Unable to count on the courts, Democrats have been studying obscure legislative maneuvers that could block Bolling votes. Anticipating that, Republicans have had their noses in parliamentary rule books as well.

Both sides have dug so deeply into the nitty-gritty of procedure that they’ve found themselves puzzling over questions such as, “What rules does the Senate operate under when it is adopting its rules?” Rules from the last session? “Robert’s Rules of Order”? Jefferson’s “A Manual of Parliamentary Practice”?

None of the above, said Susan Schaar, clerk of the Senate. She said it’s “general parliamentary procedure,” which, as it happens, is not written down.

One maneuver Democrats have considered: If Bolling votes on organization, a Democrat would stand and declare, “Mr. President, I challenge the ruling of the chair.” That would force the Senate to consider, as a point of order, the propriety of his vote.

As the subject of the challenge, Bolling would have to recuse himself, so a motion to uphold his right to vote would fail on a 20-20 party-line vote, Democrats theorize. Yet Republicans are just as certain that Bolling need not recuse himself, a view Schaar shares.

Even amid all the strategizing, some Democrats were slowly adjusting to the idea that they’ve lost control of the chamber they’ve ruled since 2008.

After the election, Richard L. Saslaw (D-Fairfax) and Thomas K. Norment (R-James City) claimed to be Senate majority leader. Saslaw said last week that he’ll drop the title, but insisted that Norment, who did not return calls seeking comment, should, too.

“Nobody’s the majority leader when there is 20-20,’’ Saslaw said.

Bolling conceded in a statement last week that he lacks the power to vote on some matters, including the budget. That’s because the Virginia constitution specifies that only “members elected” to the Senate may do so.

But Bolling reasserted his right to vote on organization, an issue on which the constitution is silent. Even some Democrats think that Bolling is on firmer ground on organization than he was with the budget.

“That’s sort of a gray area,” said Sen. Phillip P. Puckett (D-Russell). “He may be right.”

Bolling’s decision to bow out of budget votes could give the Democrats new leverage for power-sharing, since Republicans will need at least one Democratic vote for passage, said Sen. Charles J. Colgan (D-Prince William). Yet in the next breath, Colgan said that leverage comes “in spite of the fact that we are going to be in the minority.”

Pressed to say which party he thinks will control the Senate, Colgan said: “Shoot, I don’t know. I’ve been in the minority. I’ve been in the majority. It’s a whole lot more fun to be in the majority. That’s why it’s so important to fight so hard for the majority.”