A White House proposal for the U.S. Securities and Exchange Commission to absorb an independent audit watchdog faces long odds, but it could reduce resources dedicated to regulating public-company audits if signed into law, former regulators say.

President Trump’s proposed $4.8 trillion budget, released Monday, includes a provision to consolidate the responsibilities of the Public Company Accounting Oversight Board under the SEC starting in 2022, essentially making the PCAOB a department of the SEC.

The proposal faces a big hurdle: Democrats control the House, and spending bills in the GOP-led Senate need bipartisan support. As a result, few expect the proposal to pass. But its inclusion in this year’s budget request could foreshadow potential changes if Mr. Trump wins re-election in November, and if Republicans win control of Congress.

The provision would likely require an amendment of the Sarbanes-Oxley Act of 2002, which created the PCAOB in response to accounting scandals at Enron Corp. and other now-defunct firms. The oversight board—a nonprofit established by Congress, funded by fees and overseen by the SEC—is tasked with inspecting audits, writing audit standards and taking enforcement action on violations by audit firms.

Rep. Bill Huizenga (R., Mich.) Photo: Zach Gibson/Bloomberg News

Moving the PCAOB under the SEC would reduce ambiguous or duplicative regulations, the White House said. The SEC has made efforts in recent months to propose changes to existing regulation on corporate disclosures, auditor independence and other topics, in part to reduce redundancies.

Critics of the provision say it would weaken oversight of large auditing firms such as Deloitte, Ernst & Young, KPMG and PricewaterhouseCoopers, which are paid by the companies they audit and can be exposed to conflicts of interest.

“The independence of the PCAOB is very important,” said Arthur Levitt, a former SEC chairman. “It would be a mistake to fold it into SEC.” Mr. Levitt said the proposal was “representative of the deregulatory overkill that the country is experiencing now.”

The SEC and PCAOB share regulatory enforcement authority over auditors, but they coordinate enforcement to avoid duplicating efforts. Moving the PCAOB’s functions under the purview of the SEC would likely nullify the PCAOB’s five-member board, former PCAOB officials say.

Rep. Brad Sherman (D., Calif.) Photo: Andrew Harrer/Bloomberg News

Former regulators fear the proposal would reduce the total resources available for auditor oversight, as the SEC would receive only part of the PCAOB’s funding. The White House projects the SEC’s total outlays would rise by $78 million between 2021 and 2025, to $2.12 billion. It is unclear how much of that increase would be devoted to the development and enforcement of audit standards and the inspection of audits.

Assuming the budget proposal isn’t adopted by Congress, however, the White House projects that the PCAOB alone would have $325 million to spend in 2025.

A White House official said that the 2025 forecasts are estimates and that the Office of Management and Budget will continue to work with the SEC to determine appropriate funding levels. Overall spending would likely fall after consolidating the two regulators due to operational efficiencies, such as the elimination of duplicative information-technology systems and administrative functions.

“There are no contemplated reductions in auditor oversight,” the official said. “This is a big win.”

Lawmakers have taken an increased interest in the role of the PCAOB. The House Financial Services subcommittee on investor protection, entrepreneurship and capital markets in January questioned PCAOB Chairman William Duhnke about its practices, including its relationship to its overseer.

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Rep. Bill Huizenga (R., Mich.) said he had encouraged the White House to look into consolidating the PCAOB’s authorities into the SEC. “This is a conversation we need to have,” he said in an interview. “And it makes sense to me as we are trying to streamline and make government more efficient.”

But he also expressed doubts about the proposal’s chances of becoming law. “By law, the White House proposes a budget. By tradition, Congress ignores it,” Mr. Huizenga said. “But it is worth having the conversation.”

Rep. Brad Sherman (D., Calif.), who chairs the House Financial Services subcommittee on investor protection, was skeptical about the provision.

“My initial reaction is I’m not sure this is something we need to do,” he said. Mr. Sherman said he plans to study the structure of the PCAOB before making up his mind on the provision.

Representatives for the SEC and the PCAOB declined to comment.

The SEC in October named Commissioner Hester Peirce to head the regulator’s coordination efforts with the PCAOB, in an effort to better ensure the quality and reliability of financial statements. A spokesman declined to comment on Ms. Peirce’s behalf.

The SEC also last year appointedHarvey Pitt, a former agency chairman, to review the PCAOB’s corporate governance.

Shared regulatory responsibility over auditors constitutes a small subset of the SEC’s total enforcement duties, said Daniel Goelzer, a retired partner at law firm Baker McKenzie and former interim chairman of the PCAOB.

“Overlap is not a real risk because, at the end of the day, the SEC is in charge,” Mr. Goelzer said.

Write to Mark Maurer at mark.maurer@wsj.com and Paul Kiernan at paul.kiernan@wsj.com