A $45 million hole in this year’s budget is the result of a disagreement between state and federal officials over how much the federal government should reimburse Connecticut for Medicaid spending for clients who became eligible under Obamacare.

Benjamin Barnes, the governor’s budget director, reported last week that the state’s budget deficit had grown by nearly $72 million to $133 million. More than half of that deficit growth came from $45 million in lower-than-anticipated Medicaid payments.

The dispute behind the $45 million in question centers on how to determine how much the federal government should pay for medical care received by people eligible for Medicaid because of the federal health law.

The federal government pays Connecticut 50 cents for every dollar it spends on care for most Medicaid clients. But beginning in 2014, the reimbursement rate rose to 100 percent for poor adults without minor children who were newly eligible because of Obamacare.

Connecticut was the first state in the country to expand Medicaid as part of the health law, beginning the coverage expansion in 2010. The federal reimbursement rate for their care rose from 50 percent to 100 percent as of Jan. 1, 2014.

But what if one of those clients went to the hospital in 2013, but the state didn’t pay the bill until 2014?

Connecticut officials have asked the federal government to base the reimbursement percentage on the date care was paid for, rather than when the service occurred. That is, as long as the state paid the bill after the start of 2014, the federal government would pay the full cost, even if the care were delivered in the previous year.

But federal officials have maintained that to qualify for the full reimbursement, the care must have taken place on or after Jan. 1, 2014.

Barnes wrote that the state is considering options for appealing the federal government’s decision.