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“It is abundantly clear that we can organize the Republican legislature,” Mr. McDougle said. “It’s pretty settled.”

A majority of elected senators is required for a quorum to do business, giving Democrats the option of simply not showing up, which happened earlier this year when the Wisconsin Legislature was voting on controversial legislation to sharply curb the collective-bargaining power of public-sector unions.

But that’s not going to happen, Mr. Saslaw said.

“We will be there,” he said. “Inevitably, they had to show up. We’re not asking for a lot. We’re just asking for what they asked for 16 years ago; nothing more, nothing less.”

Gov. Bob McDonnell, a Republican, agreed with his party Monday, while leaving the specifics to the assembly’s upper chamber.

“It is 20-20,” Mr. McDonnell said on a conference call from New Delhi, where he was completing a two-week trade mission. “But on [organizational] matters in the Virginia Senate, the lieutenant governor breaks the tie vote.”

Mr. McDonnell stressed that, as he has done for the past two years, he would continue to work with both Democrats and Republicans on the major issues facing the state but described the issue as “an internal organizing matter for the Senate.”

“In terms of the internal workings of the Senate … I think the senators are perfectly capable of working those out,” he said.