Democrats have been critical of a push by the Treasury Department and the I.R.S. to get companies to quickly adopt the new withholding tables and warned earlier this week that taxpayers could get hit with big tax bills if they withhold too little in anticipation of the lower rates. Senator Ron Wyden of Oregon and Representative Richard E. Neal of Massachusetts, the top Democrats on the Senate and House tax writing committees, sent a letter to the Government Accountability Office asking it to analyze the 2018 withholding tables and determine whether they will result in “systematic under-withholding.”

Mr. Mnuchin on Thursday said that the release of the new tables had not been rushed and that the I.R.S., which is under the umbrella of the Treasury Department, wants taxpayers to withhold the correct amount of money.

“I think this is another ridiculous charge,” Mr. Mnuchin said at a briefing at the White House. “Our objective is not to have taxpayers over-withhold so they owe money at the end of the year.”

While companies and workers try to figure out the new tax landscape, states are trying to mitigate some of the tax hits in the law. California, New York and New Jersey are among the states that have been considering changes to their tax codes to blunt the pain that their residents could feel from the scaling back of the state and local tax deduction in the new law. States have considered switching to a payroll tax system or classifying local taxes as charitable contributions so they can be deducted at the federal level.

Mr. Mnuchin would not say if the administration would try to halt such efforts, but he assailed the strategy as being in bad faith.

“I think it’s one of the more ridiculous comments to think you can take a real estate tax that you’re required to make and dress that up as a charitable contribution,” Mr. Mnuchin said. “I hope that states are more focused on cutting their budgets and giving tax cuts to their people in their states than they are on trying to evade the law.”

Trump administration officials continued to point to corporate announcements of pay increases and bonuses to promote the early success of the tax cuts. Mr. Mnuchin on Thursday singled out wage increases at Walmart as a sign that Mr. Trump’s policies were working. However, he declined to accept any blame for the store closings and expected layoffs that Walmart announced at its Sam’s Club chain.

Mr. Mnuchin also dismissed questions about Mr. Trump’s tax returns, which he has refused to release. Democrats have said that he should make his returns public so that voters can see if he is benefiting from the tax cuts.