When most people think of Medicaid recipients, the families of doctoral candidates at well-heeled private universities like New York University don’t usually come to mind.

They should.

NYU graduate student Michelle O’Brien, for example, earns $12,000 as a teaching assistant in her field, sociology.

She can’t afford NYU’s health plan for her partner and child — which would cost $13,500.

O’Brien and her family must rely on Medicaid.

But, the need for Medicaid coverage also prevents her and her partner from marrying. If they did, they would no longer qualify under the different eligibility standards for married couples,

That’s why O’Brien joined her fellow teaching assistants at the university in forming a union.

Union representation for graduate student employees is fairly common at public universities outside of the South. But NYU is the first private university in the country whose graduate employees are unionized.

Private universities have fought unionization by teaching assistants on the basis that they are primarily students rather than employees.

The National Labor Relations Board has gone back and forth on the matter.

NYU’s teaching assistants first voted to unionize in 2000 and two years later signed a contract. But in 2004 the NLRB reversed one of its earlier rulings and said graduate student employees have no right to unionize. That allowed NYU to crush the union, with graduate employees promising to keep up the fight.

One strike and eight tumultuous years later, NYU and the Graduate Student Organizing Committee announced in the fall that they had reached an agreement. In exchange for the organizing committee dropping its challenge to the NLRB ruling, the university agreed to voluntarily recognize the union if a majority of graduate employees voted for it.

The results of that election were announced on Dec. 11: a 620-to-10 vote in favor of joining the United Auto Workers.

Labor unions said the need by teaching assistants to unionize has become more pressing as universities increasingly rely on graduate students to teach courses.

Graduate employees in 2007 accounted for 41 percent of instructional staff at public universities and 21 percent at all public and private colleges and universities combined, according to a report by the American Federation of Teachers, which represents graduate employees at public universities.

At some research universities, a majority of introductory undergraduate courses are now taught by teaching assistants, AFT Higher Education Director Craig Smith said.

“They are effectively the undergraduate teaching workforce at research institutions,” Smith said.

“To say that graduate employees are just students is absurd,” agreed Maida Rosenstein, the president of UAW 2110, the union local that now represents the NYU graduate employees.

Unions hope that the success of the drive for collective bargaining at NYU may open the door to similar efforts at other private universities, bringing private-sector graduate employees the benefits long enjoyed by their unionized colleagues in the public sector.

Graduate-employee unions at public universities have negotiated agreements over pay, health care, child care and rights for domestic partners and spouses.

They have also won pedagogical training to better prepare them to teach undergraduates, Smith said, adding that this shows how the unionization of teaching assistants can help to improve the quality of education at universities.

Conversely, the financial stress on nonunion graduate student employees can affect their teaching, O’Brien said.

“The stress caused by issues like pay, health care and working conditions has an impact on the level of attention we’re able to bring to students,” she said. “Graduate employees with outside support are able to devote more attention to grading and meeting with students.”

A fellow graduate student in sociology, Jonah Birch, said the new union means an end to unilateral decisions by the university about graduate employee stipends and pay.

Students “are paying several thousand dollars each to take your course and you’re only getting $5,500 or less,” Birch said. “Who protects you? People have families. You’re trying to pay rent in New York City.”