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“This budget bill will be devastating for Arizona in so many regards,’’ the governor said just hours after the U.S. Senate gave its approval to the package. And top of that list, she said are “the hundreds of thousands who are going to lose their health care’’ as a result of cuts being made in federal Medicaid spending.

But Hobbs said affected Arizonans should not look to the state.

“We don’t have the capacity to mitigate the cuts,’’ she said.

The problem actually could be deeper than a reduction in federal funding for Medicaid. There also are cuts to the Supplemental Nutrition Assistance Program, informally known as food stamps.

But that’s just half of the equation. What also could be in danger are the revenue figures used in preparing the state’s $17.6 billion spending plan.

What’s in the bill approved by the Senate is an increase in the standard deduction that seniors can take to reduce their reported income. That’s designed to compensate them for the federal income taxes they owe on their Social Security benefits.

And there also are provisions exempting tips and overtime from federal earnings.

What makes that important is Arizona is a “piggy-back’’ state: When Arizonans are computing their state income taxes, the starting point is the federal adjusted gross income.

Put simply, the reductions in what Arizonans are reporting on the federal form translate out to a lower bottom line in what gets filed with the Arizona Department of Revenue on the amount of income that is subject to state income taxes. And about a third of the budget is built on personal income taxes.

Hobbs, questioned about the Senate-passed bill, did not address the revenue side of the equation. Instead, she focused on the harms that the federal spending cuts will have on Arizonans.

It’s not just going to affect those who will lose Medicaid benefits. There are concerns that the loss of the federal dollars will have a disproportionate impact on rural hospitals, which depend on Medicaid.

“Hospitals and health care centers will have to close,’’ Hobbs said, leaving patients without local options.

Still, the governor left the door open to the possibility that the state may be able to do something — she’s not exactly sure what — if some version of the federal bill becomes law.

“We’re going to have to look at that when it happens,’’ she said.

“The bill keeps changing, the impact keeps changing,’’ Hobbs continued. “And I don’t know what came out of the Senate can get through the House.’’

The governor’s comments came as she did a “ceremonial’’ signing of the same budget she actually had penned her approval to last week in her office. This was more meant not just for the TV cameras but also for both more than 100 lawmakers, lobbyists and others she invited to the event who had pushed for one or more provisions in the final package.

It also provided a chance for the governor, facing what could be a tough reelection campaign next year, to explain what remains to be done — presumably under her direction.

“This budget moves us in the right direction but it’s not the end of our efforts,’’ she said. “Arizonans can trust that I will continue to fight for the things that will actually improve our lives and provide you with the opportunity to support your family, the security to sleep peacefully at night, and the freedom to choose a path that works best for you.’’