Office of Management and Budget Director Mick Mulvaney holds a briefing on President Trump's FY2018 proposed budget in the press briefing room at the White House in Washington, May 23, 2017.

President Donald Trump's budget proposal this week has some potentially major implications for the housing market.

Within the details of the $4.1 trillion spending plan is a change in language regarding government-sponsored enterprises. Specifically, the budget calls for improvements in the housing finance system, but not for the elimination of Fannie Mae or its sister agency Freddie Mac.

That's an important position shift from Trump and deviates from the course former President Barack Obama wanted to follow, according to banking analyst Dick Bove.

"There are significantly different wording changes in the 2017 budget proposal submitted by President Obama and the 2018 proposal submitted by President Trump related to Fannie Mae. President Obama clearly states his desire to get rid of this company. President Trump makes no such statement," Bove, vice president of equity research at Rafferty Capital Markets, said in a research note this week. "This is a major change in policy."

Fannie and Freddie had served as the cornerstone of U.S. mortgage finance before the financial crisis. The agencies bought mortgages on the secondary market and provided a vital backstop for banks by assuming the risks associated with home loans.

However, the financial crisis changed that. The agencies ran into financial trouble when loans to less-qualified buyers defaulted, requiring a government bailout that triggered public outrage.

Fannie and Freddie then were effectively nationalized during the crisis and have been pushed to tighten mortgage quality.

In an interview with CNBC last week, Bank of America CEO Brian Moynihan lamented that he would like to see down payment requirements for mortgages at 10 percent rather than 20 percent. However, unless the secondary market is willing to take on loans with a higher loan-to-value level than 80 percent, that is unlikely to happen.