(CNN) Republican leaders in the Virginia House of Delegates argue in legal motions that Democratic efforts to compel a circuit court to reconsider its decision allowing a questionable ballot to be recounted are frivolous and are delaying the organization of the new House for the coming legislative year.

The decision forced the 94th District race between incumbent Republican David Yancey and Democrat challenger Shelly Simonds into a tie. That set the stage for a historic lot draw where the names of both candidates would be placed into film canisters and then drawn from a bowl, with the winner the first name drawn.

Republicans also sent the chair of the Virginia State Board of Elections a letter requesting that a lot draw be scheduled by January 9.

The board said Friday that it will convene at 11 a.m. January 4 and proceed with the draw unless the court intervenes. The General Assembly is scheduled to begin its work on January 10.

A lot is at stake for Republicans. If their candidate wins the draw, they will hold on to a one-seat majority in the House of Delegates and retain control of the speakership and the majority on committees. If Simonds is declared the winner, the House would be split 50-50 between the parties and they would share power. It would be the first time in more than two decades that Republicans did not control that branch of Virginia's government.

"Make no mistake, this is a deliberate strategy to make it more difficult for the House to organize smoothly, to improve their negotiating position," Republican leader Del. Kirk Cox charged during a conference call with reporters.

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"They've sought to litigate their way to victory and try this case in the court of public opinion versus what the law says," he said, referring to Democrats.

Cox suggested that delaying the seating of a delegate could lead to an interruption of the government's work and cause problems with the inauguration of the new governor, Democrat Ralph Northam, on January 13 and the final State of the Commonwealth Address by the outgoing governor, Democrat Terry McAuliffe.

The Republican leader said his party has every intention of organizing on the first day of the new session, even if there are only 99 members seated. Under that scenario, the GOP would retain control of the House and would be able to elect a Republican speaker and avoid having to work out a power sharing agreement with the Democrats.

"If you don't organize on the first day, it makes it very difficult to carry through with those functions that are very important," said Cox, who stands to become the next speaker of the House if Republicans hold the majority.

Democrats have argued that the Republican move to introduce the questionable ballot at the Circuit Court level of the recount process was against the law. They believe the ballot should not be included in the final tally. Simonds had appeared to have defeated Yancey by one vote before the court decided to allow the ballot to be counted.

"We empathize with the court as the Yancey team gave no notice of their plan to re-litigate a ballot that should not have been admitted in the first place, nor did they submit written arguments for the court to review," Katie Baker, communications director for the Virginia House Democratic Caucus, said Friday in a statement. "We look forward to the court's response."

"We find it disappointing ... that House Republicans are using the inaugural festivities as a smokescreen to hang on to power," Baker said.

"The citizen-led process that included Democrats and Republicans all signed off on the votes," Simonds said last week in an interview on CNN. "You can't say, 'Well, we lost the next day and I'm so sad about it. Here, let's pull this out of the ballot box and reassess it.' Each vote can only be reassessed once."

The Circuit Court has yet to take up the Democratic motion to reconsider and has not indicated when it will.

Adding to the drama, the loser of the draw may ask for a recount, meaning the entire process could start again.

Cox left that possibility open Friday. "That may be what we have to do," he said.