Watt, an 11-term congressman from North Carolina, would replace Edward J. DeMarco as director of the Federal Housing Finance Agency.
Watt, a longtime member of the House Financial Services Committee, has been an advocate for affordable housing.
Obama is expected to announce the nomination Wednesday afternoon at the White House.
DeMarco, a career bureaucrat who has been the agency's acting director since 2009, has drawn the ire of Democrats and liberal activists for not allowing Fannie Mae and Freddie Mac to reduce the principal on mortgages it backs to help struggling homeowners avoid foreclosure.
But Republicans have praised DeMarco for acting in the best interest of taxpayers, who have pumped more than $187 billion into Fannie and Freddie to keep them afloat after the government seized them in 2008.
In 2010, Obama nominated Joseph Smith, then North Carolina's top banking regulator, to replace DeMarco, but Senate Republicans prevented a confirmation vote.
On Wednesday, Sen.
"I could not be more disappointed in this nomination. This gives new meaning to the adage that the fox is guarding the hen house," Corker said. "The debate around his nomination will illuminate for all Americans why Fannie and Freddie failed so miserably."
Corker said that before any nominee is considered to replace DeMarco, the Obama administration should propose specific plans for shutting down Fannie and Freddie.
But some Democrats and housing advocates praised the nomination, in part because Watt would replace DeMarco.
"Congressman Watt is a thoughtful policymaker with a deep background in finance and a long record as a champion for working families," said Sen.
She said it was time to remove DeMarco.
"Under DeMarco's leadership, the FHFA has refused repeatedly – often with cold indifference – to work with families struggling to save their homes," Warren said.
In March, California Atty. Gen. Kamala Harris and attorneys general from eight other states publicly urged Obama to replace DeMarco with someone who would do more to help reduce foreclosures.
DeMarco has said reducing the amount of principal owed by some homeowners could end up costing taxpayers money and encourage more defaults. He has argued that he has ordered Fannie and Freddie to take several other steps to reduce foreclosures, particularly by modifying the terms of mortgages.
The government seized Fannie and Freddie in 2008 to keep them from going bankrupt. As of March 29, the companies have received a combined $187.5 billion in bailout money.
The overall tab is less because Fannie and Freddie have paid a total of $65 billion in required dividends back to the Treasury. And the finances of both companies have improved, with both recently reporting they were profitable in 2012 for the first time in six years.
Obama's proposed 2014 budget for the first time projected a net profit to taxpayers of $51 billion through 2023 on the investments in Fannie and Freddie.
There is wide agreement in Washington that the government needed to shut down Fannie and Freddie and replace their large role in the housing finance system. But Democrats and Republicans are at odds over how much of a role the government should have.