Fannie Mae and Freddie Mac play a critical part in the housing market, buying mortgages from lenders, then packaging them into securities to sell to investors. The government seized control of both companies in 2008 as the housing market unraveled and the firms’ losses piled up.

The housing giants back half of the United States’ mortgages, and housing experts have warned that allowing them too much freedom again could lead to higher mortgage costs for consumers while enriching Wall Street investors.

“President Trump’s housing plan will make mortgages more expensive and harder to get. I’m urging the president: Make it easier for working people to buy or rent their homes, not harder,” said Sen. Sherrod Brown (D-Ohio), the ranking Democrat on the Senate Banking Committee.

Fannie Mae and Freddie Mac represent the last major unresolved business from the financial crisis, and Mnuchin has called them a top priority for more than two years. Under the plan, they would be turned back into private companies but would be required to pay taxpayers a fee for government protection. It would also open the market up to competitors for the first time.

While Democrats and Republicans support ending government control of the companies, several other plans have stalled in Congress. President Barack Obama’s administration shied away from the topic, fearful that a wrong move could disrupt the housing market and the availability of 30-year mortgages.

A senior Treasury Department official said that while the administration’s plan was extensive, the changes are designed to be “incremental and realistic.”

The issue is being closely watched by housing advocates as well as the banking and housing industries — all of which have developed their own competing proposals on what should be done with the companies. Several Wall Street hedge funds also invested heavily in the companies’ stock and bet that the Trump administration’s efforts may clear the path for them to secure significant profits.

This comes at a time when many U.S. home buyers are already struggling to find affordable homes. Prices have been rising for years, and there are not enough moderately priced homes for sale, according to National Association of Realtors data.

Most of the Trump administration’s proposals require action by Congress, but the Federal Housing Finance Agency (FHFA), the regulator for Fannie Mae and Freddie Mac, could take some actions on its own. The agency is run by Mark Calabria, formerly Vice President Pence’s chief economist.

Calabria, without congressional approval, could end the government conservatorship of the companies and do away with a requirement that Fannie Mae and Freddie Mac send most of their profits to the Treasury Department, for example.

“It is, after 11 years, time to bring the conservatorships to an end,” the proposal says. “Ending the conservatorships is a critical step to reducing that government influence” on the housing market.

The plan leaves many questions unresolved, including what would happen to the thousands of shares of Fannie and Freddie stock owned by the government.

The reports are comprehensive but leave it to Congress and regulators to figure out many of the details, said Guy Cecala, the publisher of Inside Mortgage Finance. “Like a lot of things, the devil is in the details,” he said.

It could take years for Fannie Mae and Freddie Mac to build up enough capital to be sustainable as private companies again, Cecala said. And it would require the Treasury Department to forgo billions a year in profits from the companies that currently flow into government coffers. “I don’t know,” he said. “Given our deficit, I would be reluctant to do it.”

Over the past decade, Fannie Mae has received $119.8 billion in taxpayer bailouts, with Freddie Mac receiving $71.6 billion. But as they returned to profitability, the companies have sent a combined $300 billion in dividends to the Treasury Department.

The Trump administration’s plan attempts to reduce the government’s influence on the housing market by shrinking Fannie Mae and Freddie Mac’s roles. It also calls for a smaller role for the Federal Housing Administration, which currently backs about 15 percent of home purchases.

Fannie Mae and Freddie Mac would pay taxpayers a fee in return for a government guarantee in case they fall into financial trouble again. But taxpayers would be forced to bail out the companies again only in “exigent circumstances,” according to the 53-page proposal.

The proposals also include several measures that target affordable housing. One administrative change urges the FHFA to “revisit … underwriting criteria” for loans on multifamily properties where rent control laws “or other undue impediments to housing development” are in place.

The housing agency should also take administrative action to come up with “more efficient mechanisms” for Fannie Mae and Freddie Mac to achieve required affordable-housing goals, the proposal states. And the document calls on Congress to pass new laws that would replace statutory affordable-housing goals “with a more efficient, transparent and accountable mechanism for delivering tailored support” to lower-income, rural and first-time home buyers.

The Department of Housing and Urban Development released a separate report that calls for the Federal Housing Administration, which backs loans to low-income and first-time home buyers, to “refocus” on its core mission. FHA-backed loans have gotten bigger and riskier since the financial crisis, the HUD report says. Homeowners are also increasingly using the program for cash-out refinance deals, the report says.

Those trends should be monitored and Congress should limit homeowners ability to use the FHA to strip equity from their homes, the report recommends.

HUD also calls for the FHA to help companies that participate in their programs avoid hefty fines for trivial issues, which the agency says has pushed some lenders out of the market. Lenders have complained about “minor errors leading to exposure to severe financial penalties,” the report says. Congress could also allow HUD to issue shorter suspensions for minor infractions, the report says.