Nashville ? They are tough, burly men. They sat in a smoky meeting room at the Ramada Inn a few miles from the airport, preoccupied with finding prison space for criminals, shutting down the rural methamphetamine labs where household chemicals are being transformed into highly addictive drugs and, in lighter moments, planning the annual golf outing and pistol shoot.

But when Phil Bredesen, the Democratic candidate for governor, turned up at the meeting of the Tennessee Sheriffs Assn. the other morning, the second question he was asked was about a different subject entirely: state taxes.

Bredesen, the two-term mayor of Nashville, made it clear he isn’t going to push a state income tax. But the prominence of the question made it clear that all politics this autumn in Tennessee is tax politics.

There is a variation of that theme in nearly all the 34 gubernatorial races being conducted across the country. The weak economy has produced revenue shortfalls in four-fifths of the states, helping to account for a combined budget gap of about $40 billion. That’s a shortfall of nearly 8 percent far higher than the gap during the last period of economic distress nearly a dozen years ago.

The revenue drops are occurring at a time when states’ health-care costs, which the National Association of State Budget Officers estimates accounts for 20 cents of every dollar of state expenditures, are climbing at dramatic rates about 25 percent in the past two years. Here in Tennessee, which leads the nation in the per capita use of prescription drugs, the rate of growth of health-care expenditures is by far the highest of any state in the Southeast.

So while Bredesen and his Republican rival, Rep. Van Hilleary, have taken positions on scores of issues, the gubernatorial election here in Tennessee is coming down to the question that has dominated state politics since the very first days: money and whether to take in more of it.

Hilleary, 43, is a Republican of the modern sort, elected in 1994 as part of the Newt Gingrich revolution, and he’s making his opposition to the income tax (and his conviction that an income tax would be unconstitutional) the centerpiece of his campaign. “You need a minimum level of taxation because you need a minimum level of government,” Hilleary said in an interview. “But I don’t think taxes and more government is the answer to every problem.”

Bredesen, 58, won’t rule out an income tax in his second term he said in an interview that eight years is too long a period to make a blanket commitment but said he believed the state’s outlook and economic structure needed to be changed. The state, he said, could not survive with what he described as “Massachusetts services and Tennessee taxes.” And he expressed worries that much of Tennessee’s recent growth came from the sewing, assembly and light manufacturing jobs that migrated here in the past two decades from the Northeast because the labor was cheap and the chances of unionization were slim jobs that, he said, were peculiarly vulnerable to being moved offshore.

At the heart of the state’s budget structure is one stubborn fact: Tennessee is one of nine states that doesn’t have an income tax, though the state does tax dividend income and interest on certain bonds at a rate of 6 percent. In his second term, Republican Gov. Don Sundquist, a onetime Memphis congressman known as an instinctive opponent of taxes, changed his mind in the face of continuing budget crises and embraced the notion of an income tax. The legislature, however, resisted several income-tax proposals. Instead, state lawmakers this July passed a tax package including a penny increase in the sales tax (except groceries), giving Tennesseans one of the highest sales tax rates in the country. (Only a couple of counties in Oklahoma have higher sales tax rates.)

Some budget experts believe that sales-tax increases generally only stave off economic crises rather than solve them. Tennessee, which relies more on the sales tax than any other state, is especially vulnerable to continuing budget problems. Tennessee also borders eight states, permitting many residents to cross into adjoining states and make purchases, for example, in Georgia, where the base sales tax rate is only 4 percent.

“Tennessee has a structural deficit our growing needs simply can’t be financed with the existing tax structure and it’s not going away and may have even worsened with the increase in the sales tax,” says Stanley M. Chervin, an independent tax consultant. “We can postpone this long-term problem, and in the gubernatorial race the candidates aren’t tackling it. They are staying away from the issue like the plague.”

But the issue isn’t staying away from them. Hilleary is throwing the income-tax question at Bredesen at every opportunity one of his ads shows Bredesen, a former Lexington, Mass., resident, talking about taxes in front of the Minute Man statue 32 years ago and the issue is surfacing in state-legislative elections this fall.

Right now polls show the gubernatorial race is a dead heat. But the voters and the candidates know that more than the election is unresolved. The future of Tennessee’s economy is unresolved as well.

David Shribman is a columnist for The Boston Globe.