A handful of early tax filers are seeing unexpectedly low refunds, or worse, owing money to the IRS. But not everyone is in for an unpleasant surprise.

Many people are watching this tax season more closely than usual because it's the first time the Tax Cuts and Jobs Act is in effect for a full tax year. The new law, passed in December 2017, enacted a number of broad changes. It introduced new tax brackets, included an expanded child care credit and changed the way itemized deductions are factored in, for example.

Unfortunately, 28 percent of Americans don't understand exactly what's different, and almost half have no idea how the changes affect their tax bracket. Adding to that confusion, refunds dropped 8.7 percent over the first two weeks of filing season, according to the Internal Revenue Service (IRS). Plus, the IRS is processing returns at a slower pace than usual, in large part due to the 35-day partial government shutdown.

"The law is so different, we may have a different pattern than in the past," Howard Gleckman, a senior fellow in the Urban-Brookings Tax Policy Center, tells CNBC Make It. "This is not a normal year."

But while some Americans may see lower refunds, most tax experts expect the refund rate to stabilize. And for some, their tax refunds will be higher this year.