MADISON, Wis. — Opponents of Wisconsin’s Republican Gov. Scott Walker submitted nearly twice as many signatures Tuesday as required to force a recall election, but still face the challenge of transforming public outrage over his moves against unions into actual votes to oust him from office.

If Walker is worried, he’s not showing it: As the petitions were delivered to election officials, Walker was out of state raising money to defend himself and the agenda that has made him a national conservative hero.

The 1 million signatures that United Wisconsin, the coalition that spearheaded the effort along with the Democratic Party, said were collected far exceeds the 540,208 needed and amounts to 23 percent of the state’s eligible voters.

Walker was elected in 2010 as part of a national Republican tide, and quickly angered unions and others with aggressive moves that included effectively ending collective bargaining rights for nearly all public workers.

Recall circulators in neon vests who were turning in the petitions Tuesday surrounded a U-Haul truck filled with boxes of documents. The group held hands and formed a line leading toward the office of the Government Accountability Board, as some protesters yelled anti-Walker chants. The boxes inside the office full of petitions targeting Walker were stacked five high and 11 rows deep.

Petitioners said they were submitting about 305,000 more signatures than were needed to trigger a recall election against Lt. Gov. Rebecc Kleefisch, and said they also exceeded the number needed to force recall elections of four Republican state senators, including Majority Leader Scott Fitzgerald.

Walker’s supporters would have to successfully challenge about 46 percent of the signatures to stop a recall election, in which the governor would likely run against a yet-to-be-decided Democratic challenger.

“I don’t know if it’s insurmountable, but it would be extremely difficult,” said Joshua Spivak, a recall expert and senior fellow at Wagner College in New York.

During the recall of California Gov. Gray Davis in 2003, petitioners also turned in almost double what was needed and only about 18 percent were tossed, Spivak said. Wisconsin Democratic Party Chairman Mike Tate said given the number of signatures collected, Walker shouldn’t seek delays and instead let the vote proceed.

“Does anyone really honestly believe we’re not going to have an election?” Tate said.

Spivak said he would expect strong voter turnout for a recall election against Walker, noting that in California turnout rose from 36 percent in the general election to 61 percent for the Davis recall.