Democrats said Wednesday they would divorce their demand for more power in the Virginia Senate from the effort to pass a state budget, as members of the General Assembly returned to Richmond for a special session.

A dozen negotiators — Republicans and Democrats, delegates and senators — had been expected to begin meeting in the afternoon to draft a two-year, $85 billion state budget that can pass both chambers.

Instead, Senate negotiators met by themselves several times — including over lunch at a restaurant off Capitol Square — to discuss a Democratic wish list totaling hundreds of millions of dollars.

“We’ve got a few things to iron out yet,” Sen. Charles J. Colgan (D-Prince William) said.

Senate Democrats have voted down two budgets and threatened to scuttle a third after Republicans rebuffed their request for more committee power and increased spending in certain areas.

Senate Minority Leader Richard L. Saslaw (D-Fairfax) said Democrats were still seeking to increase their influence on committees, which Republicans in the evenly divided Senate were able to stack in their favor with tie-breaking votes cast by Lt. Gov. Bill Bolling (R). But Saslaw said that effort has been split off from the budget process.

“It’s not out the window, but it’s not part of this,’’ he said. “This strictly has to do with financing state government and where the priorities ought to be.”

The Senate Finance Committee will meet Thursday morning to unveil areas where the two sides have ironed out compromises. Senators declined to discuss details Wednesday.

Democrats have asked for what Republicans estimate to be $600 million in new spending, including $300 million for the second phase of Metrorail’s new Silver Line to Dulles Airport; $65 million for Northern Virginia schools to attract nonteaching staff in that high-dollar job market; and an unspecified amount to pay for the ultrasounds that women will have to get before abortions under a contentious bill passed this session.

“We are making progress,” Finance Committee Chairman Walter A. Stosch (R-Henrico) said. “There are several items that have not been resolved.”

Failure to pass a budget by July 1, the start of the fiscal year, could result in a partial government shutdown for the first time in Virginia history. The spending plan pays for everything from prisons, road maintenance and colleges on the state level to courts, registrars and health care locally.

In past years, the House and Senate each passed a budget and worked out differences. This time, internal Senate issues must be resolved first.

All 140 legislators will return to vote on the budget after House and Senate negotiators have a deal. House Majority Leader M. Kirkland Cox (R-Colonial Heights) said they aim to bring everyone back on Monday afternoon, but it’s unclear whether that is enough time to work out a compromise.

Earlier in the day, a coalition of progressive groups from across Virginia urged legislators to restore potential cuts to education and health care and rescind tax breaks for corporations.