As many as 3.4 million people who received Obamacare subsidies may owe refunds to the federal government, according to an estimate by a tax preparation firm.

H&R Block is estimating that as many as half of the 6.8 million people who received insurance premium subsidies under the Affordable Care Act benefited from subsidies that were too large, the Wall Street Journal reported Thursday.

“The ACA is going to result in more confusion for existing clients, and many taxpayers may well be very disappointed by getting less money and possibly even owing money," the president of a tax preparation and education school told the Journal.

While the Affordable Care Act fines those who don't have health insurance, it also provides subsidies for people making up to four times the federal poverty line ($46,680).

But the subsidies are based on past tax returns, so many people may be receiving too much, according to Vanderbilt University assistant professor John Graves, who projects the average subsidy is $208 too high, the Journal reports.

Tax preparers, who frequently advertise their ability to deliver big refunds, have been working feverishly to avoid customer anger stemming from lower-than-expected refunds due to insurance premiums. They also are trying to make sure customers understand the potential fines for not having insurance.

"Eighty-five percent of our customers get a refund," said Kathy Pickering, who directs the H&R Block Tax Institute, according to the Washington Post. "That refund could be offset by the penalty. And if that happens, they're going to be understandably angry."

The fine for not having insurance in the second year of Obamacare is $325 or 2 percent of taxable income, whichever is greater.

But the IRS is also working on a budget that limits its ability to aggressively enforce reporting on insurance.

“As always, taxpayers are responsible for the accuracy of the information on the tax returns that they sign," an IRS spokesman told the Journal.