PHOENIX — Gov. Janet Napolitano hopes to use the awarding of a $50 million grant to the University of Arizona to convince legislators to keep spending money on higher education, regardless of the deficit.

 Napolitano, in announcing the grant this past week, said the school and its Bio5 Institute never would have received the money from the National Science Foundation if lawmakers had not approved borrowing more than $400 million to construct research facilities at the state’s three universities. And the governor pointed out that decision to borrow was in 2003, when the state was looking at a deficit, just as it is now.

 That, said Napolitano, should “absolutely ‘’ influence lawmakers as they debate how to balance next year’s budget, with a projected deficit of anywhere between $1.2 billion and $1.7 billion.

 In her budget request for the coming year, Napolitano is asking lawmakers to approve borrowing to accelerate several capital projects at state universities.

 First, she wants $470 million to complete the Arizona Biomedical Campus. That joint project of UA and Arizona State University includes training for doctors, pharmacists and nurses.

 On top of that Napolitano has a list of other specific projects she wants financed through bonding. These include $70 million for an Environment and Natural Resources building at UA and another $44 million for a Social and Behavioral Science building on the same campus.

 She also has various projects for the other two universities, including $100 million to expand the Health Professions Facility at Northern Arizona University and nearly $24 million for a School of Construction at ASU.

 Napolitano said the new grant to study plant biology would not have happened had the state not embarked on a similar borrowing path five years ago.

 “That gives them the facility and facilities that they need to show to the grant makers to say, ‘Not only do we have the scientists who can do this research, we have the buildings, we have the laboratories, we have the computer infrastructure,’ all the things that go into these very, very competitive grant processes,’’ she said.

 Napolitano also said the willingness of Arizonans to raise their own taxes also contributed to the grant.

 A 2000 ballot measure hiked the state sales tax by six-tenths of a cent, to 5.6 percent. While most of those funds go to K-12 education, UA spokesman Paul Allvin said $5 million a year has paid to keep the Bio5 Institute operating.

 But the arguments have not convinced Rep. Russell Pearce, R-Mesa, who chairs the House Appropriations Committee. He said the state’s current financial situation makes borrowing risky.

 And Pearce said if the UA got some outside money as a result of the last round of borrowing, it should use some of that to repa the state, something that is not going to occur.

 Napolitano said that, money aside, investing in education to do this kind of research is important.

 “In the end, what we’re talking about is science to be put to work to improve the quality of people’s lives,’’ she said. “If you wear clothing, if you eat food, there you go.’’

 Overall, Napolitano proposes to balance next year’s budget largely with a combination of short- and long-term borrowing, taking some cash from the state’s “rainy day fund,’’ and proposals to raise additional cash through things like ticket revenues from photo radar units. And her revenue projections are about $700 million higher than those of legislative staffers.

 By contrast, the budget option being pushed by the heads of the House and Senate Appropriations use some rainy day fund dollars but propose sharp spending cuts and no new borrowing.