Just hours after Lt. Gov. John Sanchez publicly launched his campaign for U.S. Senate, the fur started flying Tuesday in the Republican primary.

Sanchez, 48, received a sharp elbow in the ribs from his chief primary opponent, former Congresswoman Heather Wilson. But more surprising was a statement described by Politico as "icy," from his recent running mate, Gov. Susana Martinez.

And one Republican state senator, who has endorsed Wilson, even called upon Sanchez to resign as lieutenant governor.

"In the previous eight years the executive branch was always running for something else," said Sen. Clint Harden of Clovis in a statement Wilson posted on her Facebook page. "New Mexico needs leaders who stay home and take care of business for a change. The lieutenant governor's role is important especially as we do redistricting and we have some big problems in the state that need real focus. I think if Lt. Gov. John Sanchez wants to run for the U.S. Senate, he should resign."

Harden was referring to former Gov. Bill Richardson, who sought the Democratic nomination for president in 2010, and former Lt. Gov. Diane Denish, who was the Democratic nominee for governor last year.

After declaring that she wouldn't be endorsing any Senate candidate "at this time," Martinez in a written statement said, "It is Lt. Governor Sanchez's decision to pursue what he believes is a once-in-a-lifetime opportunity to run for the Senate. However, it is my responsibility to keep my word to the people of New Mexico by pursuing the reform agenda I promised and delivering the results they deserve. To prevent this race from becoming a distraction, Lt. Governor Sanchez will not be given responsibilities in my administration beyond the select few provided for in the state Constitution."

In New Mexico, the duties of lieutenant governor are few. They include serving as the president of the state Senate, acting as governor when the governor leaves the state and being an ombudsman for constituent concerns.

Former Bernalillo County Sheriff Darren White, a Wilson supporter who was the 2008 Republican nominee for the Albuquerque congressional seat, commented on Martinez's statement on his Twitter account: "The way I read it, Gov Martinez just told Lt Gov Sanchez 'thanks for nothing.' Ouch!"

Albuquerque pollster Brian Sanderoff said in an interview Tuesday said that he thinks Martinez's statement "displays displeasure" with Sanchez's decision to run for Senate. He said the governor's statement implies that Sanchez is not part of her "reform agenda."

Sanchez in an interview said he "totally respects" Martinez "and her efforts to bring bold change to New Mexico." He said if he's elected to the Senate, "I'm looking forward to working side by side with Gov. Martinez on helping the state's economy and getting New Mexico back to work."

Sanchez, who owns an Albuquerque roofing company, filed his paperwork with the federal government last week. He announced his campaign late Monday with a new campaign website and a biographical video.

Though the 60-second video, which also will run as a television ad, mainly deals with Sanchez's humble beginnings and his success as a businessman, there's also a thinly disguised barb aimed at Wilson: "We don't want to return people back to Washington, D.C., who got us into this mess in the first place," Sanchez says in the spot. It was a variation on the same theme Sanchez hit upon in a March interview with The Hill, in which he said Wilson represents "policies of the past, and decisions and leaders that kind of got us into this mess in the first place."

On Tuesday afternoon, the Wilson campaign responded with an email statement: "We welcome Lt. Gov. Sanchez into the race and look forward to contrasting Heather Wilson's conservative record with his invented one. On issue after issue John Sanchez is not who he says he is, and Republican voters will be quick to figure that out."

Followers of New Mexico politics have long expected the GOP Senate primary to get nasty — as was the case in 2008 in the bitter Senate primary where Wilson lost to U.S. Rep. Steve Pearce.

Asked about Wilson's attack on Sanchez, Sanderoff said, "It shows she's learned from her mistakes in her last election in not doing enough to defend her record as a conservative."

Sanderoff noted that in 2008, Pearce and outside groups such as Club For Growth attacked Wilson as a "liberal."

But, Sanderoff said, it wasn't just the "liberal" tag that defeated Wilson. He said that Pearce, who has since been elected again to the 2nd Congressional District seat he gave up for the Senate race, won his home district by a 3-to-1 margin, while Wilson won her district by only a 2-to-1 margin.

"Sanchez may do well with conservatives, but he doesn't have that regional base." Both Sanchez and Wilson are from Albuquerque.

Lonna Atkeson, a political science professor at The University of New Mexico, agreed that Sanchez is hurt by a lack of regional base. She also said Sanchez is at a disadvantage due to lack of name recognition, especially compared with Wilson. Atkeson said polls have shown that many voters have negative feelings about Wilson, which could work to Sanchez's advantage.

But she said, "I'm not sure he has the political experience to bring in the campaign dollars, and I think Wilson does."

Last month Wilson announced that she'd raised more than $300,000 in the first three weeks of her campaign. Sanchez on Tuesday acknowledged that he's starting out at a financial disadvantage, but said, "We're still a year away from the primary. We've got ample time to take advantage of great statewide support and the large donor base that's supported me before."

Atkeson said that Sanchez needs the public endorsement of big-name Republicans like Martinez and Pearce.

But an endorsement from Martinez does not appear to be coming in the near future. And a spokesman for Pearce was noncommittal Tuesday.

"Mr. Pearce remains focused on serving New Mexico's Second District," said Eric Layer in an email. "We have a job right now tackling critical issues particularly creating jobs, addressing the debt ceiling and controlling federal spending. Those are the Congressman's current focus."

But if Republicans are wary at the prospect of another divisive Senate primary, both Sanderoff and Atkeson said Tuesday there's a good chance that the Democratic primary between Congressman Martin Heinrich and state Auditor Hector Balderas also has a good chance of turning negative.

Contact Steve Terrell at 986-3037 or sterrell@sfnewmexican.com. Read his political blog at roundhouseroundup.com.