The Treasury Department does consult the budget office on some of its rule-making, but since a 1983 memorandum of understanding, the office has not had the authority to review the Treasury’s tax guidance, on the theory that it is not economically significant enough to warrant it.

An executive order from Mr. Trump last year called for that arrangement to be re-examined. With the Treasury Department now playing a greater role in policymaking — for instance, overseeing enforcement of parts of the Affordable Care Act and trying to limit corporations from engaging in mergers to avoid taxes — Mr. Mulvaney and other White House officials think that the I.R.S. should be subject to greater accountability when making decisions that often go beyond technical clarifications.

Greater accountability, however, could come with costs.

If Mr. Mulvaney wins the argument, “it will slow the process down,” said John A. Koskinen, a former I.R.S. commissioner whose term ended last year. “If you had all the regulations coming out of Treasury and I.R.S. subject to more review and delays, it would not be making taxpayers, accountants and lawyers happy. They are pushing to get that information as quickly as they can.”

Since the passage of the tax bill late last year, negotiations between Mr. Mnuchin and Mr. Mulvaney have grown increasingly vigorous, with both sides laying claim to being the law’s final arbiter.

A change would be seen as a win for Mr. Mulvaney, who has made deregulation a priority in the White House. It would also be a blow to Mr. Mnuchin, who has been the tax bill’s most public defender on behalf of Mr. Trump, diminishing his department’s authority under his watch.

The potential change in regulatory oversight could have major implications, both logistical and political.

Adding a cost-benefit analysis by the budget office into the process would potentially add another layer of red tape — which Mr. Trump famously hates in other areas of regulation — to a process that is already proceeding too slowly for many business groups’ liking. Treasury officials are concerned that the budget office lacks the resources and tax expertise to properly assess tax guidance and that the process will get bogged down, potentially delaying rules to clarify the law for months. One early hurdle would be hiring; the budget office does not currently employ its own team of tax lawyers.