Sen. Timothy Keller and Rep. Jim White, a Democrat and a Republican, sponsored the bill aimed at changing the finance authority's leadership.
Martinez, now responsible for nine of the 11 seats on the finance authority board, said in her veto message that the bill did not address structural changes the agency needs, such as moving it under state budgetary authority and the state code for awarding contracts.
"I was extremely disappointed that those recommendations were not considered or reflected in the final version of the bill," Martinez said.
Keller had criticisms of his own, saying a chance to improve an important government agency was lost with Martinez's veto.
"It's not difficult to see why the NMFA board could miss a faulty audit," Keller said. "The current governance structure does not follow basic best practices. It suffers from a lack of expertise, high turnover and a glaring lack of diversity of interests."
He said his bill would have fixed those problems and restored confidence to taxpayers that mismanagement would not recur.
One of his biggest concerns is that the NMFA board includes four cabinet secretaries in Martinez's administration who are busy with full-time jobs.
"There is only one public member with 10 years of public finance experience and zero with current banking experience," Keller said.
For her part, Martinez said having cabinet secretaries on the finance authority was essential.
"Because of the nature of projects that are overseen by the NMFA, having cabinet secretaries or others who specialize in environment, energy, finance and economic development is not only necessary, it is vital to carrying out the mission of the NMFA," she said.
Cabinet secretaries, swamped with other obligations, often sent surrogates to finance authority board meetings until the crisis of the phony audit became public last summer.
Jon Barela, secretary of economic development, said in a previous interview that he is mandated to serve on more than 30 boards and commissions, making it impossible to attend all meetings of the finance authority. But, he said, he had confidence in his designated representative to make good decisions for the agency, which bankrolls public projects such as roads and schools for local governments.
The finance authority's ability to do business was stymied by the fake audit.
Its board members fired CEO Rick May after the scandal. Martinez said the agency was now on the upswing.
"During the last nine months, my appointees to NMFA have engineered a dramatic turnaround so that NMFA's line of credit has been restored and will be able to issue bonds again this spring," she said.
Martinez vetoed a second bill by Keller to determine the effectiveness of more than $1 billion in state tax credits. Rep. Lucky Varela, D-Santa Fe, co-sponsored the measure.
"We desperately need this information," Keller said. "Seventeen states are doing this. It is the prerequisite for meaningful tax reform and job creation."
Martinez vetoed the bill, as she did a similar one in 2011. Keller said he had addressed her past concerns, such as allowing more time to complete administrative analysis of the tax code.
Martinez said she still had concerns about the reworked bill. Chief among them was its relevance.
She called the bill "unnecessary," saying the state already has a tax expenditure report.
"I am also concerned about the potential violation of confidentiality of taxpayer information created by the bill," she said.
Keller called her veto "very shortsighted."
"New Mexicans are tired of the hemming and hawing when it comes to the effectiveness of our tax incentives," he said.