The penalty for failing to have insurance in 2014 is the higher of $95 per person or 1 percent of taxable household income, but in 2015 it will be the higher of $325 or 2 percent of income.
"We're not making a decision on that yet," said Slavitt, principal deputy administrator for the Centers for Medicare and Medicaid Services, when asked about the chance that tax filers who get sticker shock will get another crack at enrolling in insurance plans
But, "I think it would be a mistake to assume that they [will have] an opportunity beyond Feb. 15," Slavitt said. "We'll deal with special ... considerations when we get past Feb. 15."
Some consumer advocates have called on the Obama administration to align the Obamacare enrollment season with tax season, because that is the time when most Americans are getting a refund, which in turn could make it easier or more desirable to buy an insurance plan.
They have criticized the fact that open enrollment began Nov. 15, just before the holiday season, which is the time when Americans are most cash-strapped.
Read MoreObamacare sign-ups hit 9.5M
Also Wednesday, the Health and Human Services Department announced it is teaming up with some of the biggest tax preparers in the U.S., as well as nonprofit groups, to help the public understand how their taxes this year are affected by the Affordable Care Act, and what their obligations are.
The groups and companies are offering a combination of in-person assistance and online assistance during this tax season.
Large tax firms and preparation software involved in the initiative include H&R Block, Jackson Hewitt, Liberty Tax Service, TurboTax and FileYourTaxes.com, according to a press release issued by HHS. Details about the what each company and group is doing can be read here.
HHS Secretary Sylvia Burwell said, "We are working to provide taxpayers with the tools and information they need to file their returns and answer their questions."
Burwell's department has also rolled out online resources of its own to help people understand the tax effects of Obamacare, as has the Internal Revenue Service.
This year is the first that tax filers will be required to declare on their income tax returns whether they had health coverage. The ACA required people to have such coverage, be it through their employers' health plans, privately purchased insurance, Medicare or Medicaid, or face a tax penalty.
This is also the first year that people who received federal tax credits that helped them pay premiums for health plans purchased on government-run Obamacare exchanges are required to file forms that reconcile the money they received with their incomes.
The tax credits were based on estimates of annual income people made when they applied for the insurance plans, so some people will owe the government money back, and others will get more money than they did if their actual incomes were different from their estimates.
The Treasury Department does not have official estimates on how many people will owe refunds for subsidies they received, or how many people will get additional money as a result of underestimating their incomes. But the department, according to a senior official who spoke on background, expects that the majority of people who do end up owing money back from their subsidies will owe an amount that is less than what they are owed in their overall tax refund.