Senate Democrats and Republicans are opening negotiations over a plan to draw new Senate districts, in hopes of passing a redistricting plan that will be signed into law by Gov. Bob McDonnell (R).

Democrats already pushed one map through the Senate, drawn in response to the 2010 census, adopted on a straight party line 22 to 18 vote. But McDonnell vetoed the plan and legislators have returned to Richmond to try again.

Sen. Janet Howell (D-Fairfax) and Sen. Jill Holtzman Vogel (R-Winchester) both said a bipartisan group of senators would meet behind closed doors Monday night in hopes of reaching a deal over a map that could pass with votes from both parties.

Howell said senators have had some conversations with McDonnell and his staff, and she believed he would sign a plan that had met the approval of Senate Republicans.

Vogel said the meeting would take place at the General Assembly Building, “where there are maps and computers” so the group could attempt to draw a new plan.

“It’s very positive,” she said. “I think everyone is highly motivated.”

The negotiations are a significant shift from a week ago, when Sen. Majority Leader Dick Saslaw (D-Fairfax) declared Senate Democrats would not change a comma of their plan in response to McDonnell’s veto.

Saslaw told fellow senators on the floor Monday that he hoped the group could come up with a plan that would pass “with overwhelming support” on Wednesday.

Reaching agreement may not be easy though. Howell said Democrats would start the meeting by explaining that they continue to believe the map they adopted was legal and fair.

Plus, she said, one thing will not be negotiable: “We won’t negotiate away our majority.”

If the General Assembly and governor cannot agree to a redistricting plan, new maps will likely be drawn by the courts instead.