A few states are likely to come through the pandemic in comparatively good shape thanks to robust savings, tight financial controls or local economies that are insulated from the worst impacts of social distancing.

Wyoming, though dependent on energy prices, has a very large rainy day fund relative to other states. Minnesota and North Carolina have some of the highest credit ratings in the nation and foster a mix of manufacturing, education, health care and business services, according to Moody's Investors Service, the rating arm of Moody's.

Many states are pleading for more aid from Congress, which has so far sent money in its coronavirus relief packages to deal with the health crisis but not to offset revenue losses.

Congress has doled out about $150 billion in Covid-19 response dollars to state and local governments, plus some additional money to cover elevated Medicaid costs. The money sent to local governments has helped pay for needs like personal protective equipment. But it can't be used to replace revenue lost as a result of the shutdown.

In recent weeks, White House and Democratic negotiators have been discussing roughly $2 trillion in additional stimulus, but the price tag has encountered resistance in the Republican-controlled Senate amid concerns about rising debt and some of the expected provisions, and a deal is unlikely to come together before the election.

In the negotiations, House Speaker Nancy Pelosi and White House officials moved closer on many issues, including how much additional aid to provide to state and local governments, but had not yet reached an agreement finalizing an amount.

President Trump and Senate Majority Leader Mitch McConnell have said they don't want Covid-19 aid used to address longstanding financial problems. Mr. McConnell suggested in April that states should be allowed to file for bankruptcy to address their pension debt. Mr. Trump asked in a tweet that month: "Why should the people and taxpayers be bailing out poorly run states like Illinois?"

Illinois, with the worst finances of any state, has been banking on billions in federal funding. The state has a $230 billion pension liability after years of putting off payments, according to an estimate by Moody's Investors Service, and faces an additional $8 billion backlog of unpaid bills.

Since the pandemic, Illinois's total retirement and debt liabilities are on track to make up 45% of the state's gross domestic product by June 2021, up from 35% in 2019, according to Moody's Investors Service.

Illinois was one of only two borrowers to tap loans offered from the Federal Reserve as part of the aid packages. New York's Metropolitan Transportation Authority was the other.

Illinois issued $1.2 billion in notes, but the funds are expensive, with an interest rate about 10 times the level typical in the market. The state has said it could borrow more. A spokeswoman for the state didn't respond to requests for comment.

Over the past six months, there have been 51 first-time bond payment defaults, according to Municipal Market Analytics data. It's the highest level over that time frame since 2012, when a string of borrowers still reeling from the last recession ran out of money to pay their debts.

While none of the recent defaults have involved state credits, some local governments are facing repayment strains. The airport authority of Rock Island County, Ill., for example, disclosed in August that it hasn't been able to collect enough in airline ticket fees to maintain the level of cash it promised bondholders it would set aside. The authority filled in the gap with other funds, such as parking lot revenues, and may consider delaying capital projects, its executive director said.

In Connecticut, debt costs have reduced the state's spending flexibility. Before the pandemic, yearly payments on bond debt, pensions and retiree health obligations absorbed 31% of state-generated revenue, according to Moody's Investors Service, making it one of the most indebted states in the nation.

Much of Connecticut's liability stems from state efforts to shoulder the burden of its aging cities and towns. Almost a third of its total debt is local teacher pension and retiree health-benefit obligations, Moody's Investors Service said, much of it from the 1990s, when officials skimped on retirement payments.

Two years ago, the state backstopped debt issued by its capital city of Hartford, which was warning it could declare bankruptcy.

The state's hospitality and leisure jobs were down by about half at the height of the shutdowns, according to the Boston Fed, and were still down by about a quarter in August, despite a partial recovery. The state's total unemployment rate was 9.5% in August.

The flurry of homebuying as people fled New York City for Connecticut towns has had limited revenue benefits. The state's tax collections from real-estate sales surged to a 10-year high of $47 million in August, according to the state revenue services department, but total collections from April through August remain below where they were the past two years.

To address the shortfall in this year's budget, Connecticut's governor is recommending the state make about $25 million in cuts and draw on its rainy day fund. The state has avoided reducing state funding to social-service providers despite revenue losses, said Melissa McCaw, secretary of the state's Office of Policy and Management.

Groups that provide mental-health and substance-abuse treatment have received federal aid to help with Covid-related health and safety costs, but have asked for additional state help as well. Ms. McCaw said the state "will continue to monitor provider needs."

Connecticut has historically been one of the top 10 states for drug overdoses, which have increased during the pandemic, spiking higher in the first quarter of 2020 than in any of the previous eight quarters, according to the Centers for Disease Control and Prevention.

Community Health Resources, which offers mental-health and addiction services to 27,000 children and adults, is concerned it won't receive its expected more than $40 million in state funding -- 62% of the organization's annual budget -- in the next fiscal year, which begins in July.

"We are working with individuals who, were it not for our services, would be in emergency rooms," said CEO Heather Gates.

Write to Heather Gillers at heather.gillers@wsj.com and Gunjan Banerji at Gunjan.Banerji@wsj.com

(END) Dow Jones Newswires

10-28-20 1500ET