That criticism centered on the state's economy, but likely resulted from the governor's resistance to endorse the presumptive Republican presidential nominee thus far.
"He lashes out at the least bit of disrespect," Lonna Atkeson, a University of New Mexico political science professor, said of Trump.
But she said of Martinez, "She is a leader in the Republican Party and she can't just stand on the sidelines."
Carter Bundy, political director for the American Federation of State, County and Municipal Employees union, said Trump's criticism carried a grain of truth.
New Mexico's economy hasn't rebounded from the recession like neighboring states have.
The 6.2 percent unemployment rate is double that of Colorado, and the state has the highest child poverty rate in the nation at 30 percent. The overall rate is 21 percent. Moreover, New Mexico's high school graduation rate is the lowest in the nation.
Such statistics led a Catholic children's organization to conduct an ad campaign parodying the Martinez administration's successful "New Mexico True" tourism slogan.
One "New Mexico Truth" ad included the line "where we celebrate our unique cuisine and turn a blind eye to our hungry children."
Bundy noted the irony of Trump criticizing the rising number of New Mexicans on food stamps when a state agency is being investigated for trying to keep people from getting such aid.
But Martinez has celebrated success on the political front from her RGA leadership posts to victories in New Mexico's Legislature.
The governor's Susana PAC has raised more than $2.6 million, while two other super PACs affiliated with Martinez and her top political adviser, Jay McCleskey, have raised $4.2 million in recent years.
McCleskey is well paid by those PACs and worked for the RGA during the 2014 cycle. A federal grand jury investigation into some of his political dealings ended earlier this year with no charges.
The Martinez political team ousted a key Democratic Senate leader in 2012.
And in 2014, Republicans took control of the state House for the first time in 60 years, in large part based on the money spent by those PACs and strategy engineered by McCleskey.
This year, they're aiming at keeping the House and trying to gain the state Senate.
Such success, along with the allure of a being a Hispanic Republican woman, led many to put Martinez on lists of potential vice presidential nominees.
That talk subsided somewhat after a December "pizza party," where audio recordings featured the governor chastising police and a hotel clerk in an effort find out who complained about the noise from a Santa Fe hotel room.
The Trump dustup virtually ends any talk of joining his ticket for the fall run.
However, Bundy said Trump "definitely hurt himself" in the state over the controversy.
And then there's the question of party unity.
"I think that the entire Republican Party's future is unknown and uncertain," Atkeson said. "There's a bigger issue here, which is about the Republican Party and what it should be doing."
Martinez's coolness toward Trump isn't unusual in New Mexico.
The state's big money Republican donors haven't been generous to Trump, at least prior to Tuesday's $10,000-per-person fundraiser. Most of their money went to Ted Cruz, with Trump bringing in only about $14,000 from New Mexicans through the end of April.
Martinez wasn't alone in avoiding Trump this week. None of the state's elected officials shared the stage with him at the event.
Also noticeably absent was the state's lone GOP congressman, Rep. Steve Pearce.
He and Martinez differed just last weekend when Republicans ousted their current national committeeman, an ally of the governor. Pearce's wife nominated the successful challenger, former state GOP Chairman Harvey Yates, who also has criticized Martinez about the state's economy.
But Pearce has said he would endorse Trump as the nominee. The question remains whether Martinez will eventually do so, too.
She's said she won't vote for Democratic front-runner Hillary Clinton. And by resisting Trump, she is parting ways with New Jersey Gov. Chris Christie, her predecessor as RGA chairman.
But the governor's spokesman told reporters that Martinez won't be "bullied" into supporting Trump, whose bombastic political style has alienated much of the Republican establishment.
But Atkeson and Bundy believe she'll eventually come around, potentially after the New Mexico primary election next month when Trump runs unopposed in a vote with little meaning. He has now surpassed the delegate threshold for nomination, according to an unofficial tally released Thursday.
"She does represent Republican voters, and my guess is that on June 7, there are going to be a lot of Republican voters who turn out for Donald Trump," Atkeson said.