White House budget chief Mick Mulvaney said Thursday the Trump administration meant to make the tax plan outline it released vague, and assessing its long-term effects is difficult at this point.

The long-awaited proposal unveiled Wednesday did not include many key details, such as the tax rate for corporate cash repatriated from overseas. The White House was also vague about how it would pay for what it calls the biggest tax cut in U.S. history without busting the federal deficit, though Treasury Secretary Steven Mnuchin insisted economic growth and the closing of loopholes would make up for the lost revenue.

Mulvaney, a budget hawk when he served in Congress, told CNBC on Thursday "there's no way to know" yet what effect the plan will have on the deficit.

"There's no way to score what we put out yesterday. And we did it on purpose. Not to try and hide the numbers, but to say, 'Look, this is the first discussion,'" the Office of Management and Budget director told CNBC's "Squawk Box."

Mulvaney said the White House "learned a lesson" from the failed first effort led by House Speaker Paul Ryan to replace the Affordable Care Act. The administration wanted to get involved in the discussion on tax reform "much earlier," he said.

Trump's plan calls for cutting income tax brackets from seven to three, with a top rate of 35 percent and lower rates of 25 percent and 10 percent. Mulvaney said the White House is working with Congress to decide what income ranges will fall under those brackets.

The White House has signaled it will not support a border adjustment tax, a controversial revenue-raising piece of the House tax plan, as it stands. Critics of Trump's tax plan have questioned what he would do to offset the lost revenue from massive tax cuts.

Mulvaney said the White House is "looking at other ways," including the elimination of many deductions like those at the state and local level.