And Mr. Walker’s campaign portrayed its own fund-raising, in part, as a response to the other side — labor interests that have opposed Mr. Walker since he pressed to cut benefits and sharply limit collective bargaining for most public workers, moves that set off a political war in the state. A federal court struck down parts of that law on Friday. “These contributions are being used to fight the millions in out-of-state state union dollars that have been funneled into Wisconsin to fund this baseless recall,” said Ciara Matthews, Mr. Walker’s campaign spokeswoman.

Labor groups and Democrats balked at the notion that they will come close to matching Mr. Walker’s financial support, but they have a larger issue to sort out for the moment. While they coalesced around recalling Mr. Walker since last fall, gathering what state election officials concluded to be far more signatures on petitions than were required to force a recall, they have yet to settle on just one Democrat to oppose Mr. Walker.

As was widely expected, the state election officials, known as the Government Accountability Board, unanimously approved holding new elections, after workers spent weeks studying signatures on recall petitions and found that 900,938 of them were valid. Under state law, far fewer signatures — 540,208 — were needed, representing 25 percent of the total votes cast in the last governor’s race. A recall election is expected to cost Wisconsin at least $9 million to conduct.

Mr. Walker, who was elected in 2010 in a series of Republican victories that also shifted partisan control of both chambers of the state legislature, is not expected to contest the holding of the election, and has said he believed it was inevitable. In the nation’s history, only two governors have been removed through such a process — Gray Davis, of California, who was recalled in 2003, and Lynn Frazier, of North Dakota, recalled in 1921.

There is little time for Wisconsin Democrats to sort out their differences. Primary elections in state contests will take place May 8, when the Democrats will presumably settle on a single candidate to oppose Mr. Walker. Then a general election will take place on June 5.

Late Friday, Mayor Tom Barrett of Milwaukee, the Democrat who ran unsuccessfully against Mr. Walker two years ago, told supporters that he will seek the office once again. And other Democrats are already in the race, including Kathleen Falk, a former Dane County executive; Doug La Follette, the secretary of state; and State Senator Kathleen Vinehout.

In addition to Mr. Walker’s election, recalls were ordered on the same dates (presuming primaries are needed) for Lt. Gov. Rebecca Kleefisch, a Republican, and for four Republican state senators. Democrats pushed for the recalls in an effort to shift the balance in Madison. The recent resignation of a Republican state senator put the balance in that chamber temporarily at 16-16, and both sides hope to take control.

Complicating matters, Wisconsin residents are already weary from a series of divisive campaign seasons, including earlier efforts to recall state senators in both parties last summer and a nominally nonpartisan race for the state Supreme Court earlier last year. In a way, the state’s presidential primary on Tuesday has become an afterthought for voters, many in the state said.