Springfield, Ill. ? What a state takes away, it also can give back.

Less than a year after raising personal and corporate income taxes, Illinois officials are pushing a $250 million package of tax breaks for several prominent businesses threatening to leave the state, including Sears and the Chicago Mercantile Exchange. To make the measure more palatable, individual taxpayers also would get a dollop of relief.

The measure suffered a setback Tuesday when the House rejected it, but legislative leaders said they were determined to reach a deal in the coming days or weeks.

The idea of giving tax breaks to companies is a hard sell in the state Legislature when many families are struggling and the Occupy Wall Street movement is reflecting anger at corporate interests. But advocates say if Illinois doesn’t take action, the businesses and their thousands of jobs will be lured away by states that are eager to take advantage.

“If we don’t do it, another state will. That’s the reality of the world in which we live,” said Rep. John Bradley, a Marion Democrat who is chairman of the Illinois House Revenue Committee.

The Senate approved the proposal Tuesday in a special session, but the House balked, sending lawmakers into further negotiations.

“We are prepared to come back as soon as there is an agreement, as soon as we are able to work this out,” said Bradley, who has overseen negotiations. “Unfortunately, that day is not today. Whether it’s tomorrow or the next day or next week, we are prepared to come back as soon as this is settled.”

Illinois’ tax dilemma is a collision between two different goals: Balancing the budget and avoiding the image of a state that’s bad for business. And in the process, officials want to avoid being exploited by companies making threats, perhaps empty ones, to flee Illinois.