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Absentee voting began May 6, and in-person early voting started May 17.

King had broad-based geographic support in the poll, strong backing among male voters and near-equal percentages of support among Anglo and Hispanic voters. He launched his first television advertising last week.

Webber, a Santa Fe businessman, and Rael, a longtime government administrator from Albuquerque, each had the backing of 16 percent of the Democratic voters polled.

Twenty-nine percent of the Democrats said they were undecided or did not know which candidate they would vote for.

About 12 percent said they supported Morales of Silver City, while 5 percent said they favored Lopez of Albuquerque.

The winner of the June 3 primary election will face incumbent Republican Gov. Susana Martinez in the November general election. Martinez is unopposed for a second term in the GOP primary. She has amassed a sizable campaign war chest for her re-election effort.

Webber and Rael have both aired recent TV ads that have played a role in making the contest for the Democratic nomination more competitive, Sanderoff said.

“The race is not over by any means,” Sanderoff said. “You’ve got lesser-known candidates who are trying to close the gap.”

King had stronger support among male voters than among female voters, who traditionally make up the majority of Democratic primary turnout. Twenty-seven percent of male voters surveyed said they planned on backing King, compared to 19 percent of female voters.

Rael posted a strong showing in the Albuquerque metro area, where 20 percent of voters surveyed said they voted for him or planned to vote for him.

Morales, who is the only candidate from southern New Mexico, was backed by 37 percent of voters in southern and southwestern areas of the state.

Webber, who has so far raised more money than his Democratic rivals, was supported by 28 percent of Anglo voters who identified themselves as “liberal” – a higher figure than any other candidate among that voter demographic.

Webber and Morales had the highest percentages of support among Democratic voters with graduate degrees.

Hispanic voters were most likely to support King, with 23 percent of Hispanic voters saying they have voted or planned to vote for him. Rael and Morales were close behind.

Noting the nearly one-third of Democratic voters who haven’t made up their minds about the race, Sanderoff said it is typically more difficult for better-known candidates to pick up significant shares of that support. King is the best known of the Democratic candidates, and the undecided voter pattern could give hope to his Democratic rivals, Sanderoff said.

“There are a lot of proven voters that haven’t made up their mind,” said Sanderoff, who also cautioned not all those voters will end up casting ballots.

New Mexico has a closed primary election system, meaning only registered Democrats and Republicans are eligible to vote for their parties’ candidates on June 3. Meanwhile, turnout is usually low.

While there were 597,872 registered Democratic voters statewide as of May 15, only about 25 percent of eligible voters ultimately voted in the 2012 New Mexico primary election.

The Journal Poll surveyed 631 Democratic voters statewide who have voted in recent state primary elections – either in 2010, 2012 or in both years – and said they were likely to vote again this year.

The poll was conducted May 20-22. Seventy-three percent of those surveyed were interviewed via landline telephones, while 27 percent were interviewed on cellphones.

The poll has a margin of sampling error of plus or minus 3.9 percentage points.