Buying a home is not for everyone: HUD Secretary

The dream of owning a home won't be possible for all Americans, Housing and Urban Development Secretary Shaun Donovan said on Tuesday.

"Not everybody is going to be able to get a mortgage or buy a home. We need to recognize that as a country," he said on "Squawk Box," ahead of President Barack Obama's speech on housing finance reform in Phoenix.

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The president wants to act in the short-term to accelerate the recovery in housing, Donovan explained, including measures to "simplify and streamline what it takes to get a mortgage" so qualified families won't be "locked out."

"If we have safe, simple products, if we provide help to families to make sure they are making the right decision and we make sure that the loans are underwritten in the right ways, we can make safe mortgages with 5 percent down payments," he added. "So that is something we want to continue on a targeted basis to make sure that families can get access."

Donovan also stressed the importance of building a "housing finance system for the future that protects taxpayers" against the kind of lax lending standards that "got us into this bubble in the first place."

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The president realizes "the model that Fannie Mae and Freddie Mac followed didn't make sense—heads they win, tails taxpayers lose," Donovan continued. "We can't continue that model."

Obama is encouraged by bipartisan support in the Senate for winding down Fannie and Freddie, the HUD secretary said.

More than four years after the president outlined a plan to try to stop the housing market free-fall, he chose to return to Phoenix for Tuesday's speech to highlight the progress being made. The city saw home prices rise 20.6 percent in May compared to a year ago, according to the widely-followed S&P/Case-Shiller index.

By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.