While social service agencies and public universities are breathing a sigh of relief with a budget agreement in place, it will take some time for the state to unwind from a financial hole that’s left a $15 billion bill backlog.

Revenue from an income tax hike — estimated at $4.3 billion — won’t help the state immediately. The tax increase was part of a budget package vetoed by Gov. Bruce Rauner; that veto was overridden on Tuesday by the Illinois Senate and then on Thursday by the Illinois House.

According to the Illinois Department of Revenue, the additional tax revenue will come in as soon as employers begin withholding at the new rate. Larger employers are required to make semi-weekly payments, so the department should see those rates changed soon, with the revenue coming in within weeks. The department said estimated payments are due in mid-September and will reflect the new income tax rate.

The income tax hike is retroactive to July 1. And it will take a month or two for that amount to start trickling into the state, according to Illinois Comptroller Susana Mendoza’s office. A corporate income tax hike — from 5.25 percent to 7 percent — is expected to bring in about $460 million. The state won’t see those funds immediately, either.

Mendoza, the state’s check writer, is keeping the same priorities in place until more funds come in, including hardship payments, pensions, court mandates, debt service, higher education and K-12 funding.

“This is the baton that our office has been handed and we are prepared to run with it and do the best we can to stabilize our finances,” Mendoza said in a video on Thursday. “Please be assured that in the coming days, weeks and months, my office will implement this budget in a way that best protects taxpayers.”

Without a budget in place, the comptroller’s office had been abiding by court orders, consent decrees and state laws. Debt payments, pension contributions and funds for local government were required by law; a court order required the state pay state employee salaries in full.

But a federal judge earlier this month also ordered the state to pay $586 million a month for Medicaid vouchers that come in after June 30. U.S. District Judge Joan Lefkow also ordered the state to pay another $2 billion toward the more than $3 billion the state owes to managed care organizations, which process payments to providers.

The state in July 2015 was ordered to continue making Medicaid payments during the impasse. The state’s Medicaid program uses both state and federal money and totals about $8 billion a year in spending.

State universities will get some immediate funds. Appropriations for universities were held up when a partial budget expired Jan. 1. The new budget plan allows the state to dole out funds earmarked specifically for higher education, which will help them run operations and fund MAP grants for students. Universities had endured drastic cuts, which forced layoffs, furloughs and missed payments to needy students who relied on grants to attend college. It also prompted enrollment drops which the universities will have to work to regain as the state begins to catch its breath again.

A nearly $15 billion backlog will continue to be the state’s largest problem for some time to come. And if credit agencies downgrade the state’s bond rating, that feat will become even more difficult. A spending plan that was approved includes using about $3 billion in surplus revenue to to help pay off the backlog.

The Illinois comptroller’s office plans to attack the highest interest payments first. That includes past due medical bills that are racking up between 9 and 12 percent interest, according to Mendoza spokesman Abdon Pallasch. The state has more than $800 million in late payment interest penalties to pay.

Among the entities immediately affected by the agreement and granted appropriations authority to dole out funds, the Illinois Lottery on Thursday night announced it will begin to sell Mega Millions and Powerball tickets again. The games were dropped from the Illinois Lottery in late June — as legislators continued to iron out a budget deal. The state brings in about $90 million a year in revenue from the games.

And the Illinois Department of Transportation, too, has re-started construction projects. The department had warned that hundreds of projects would be halted and 20,000 workers could have been laid off without a budget deal in place.