Corker asked for some direction from the committee's leaders, ahead of a markup on an FHA compromise bill next week, on how they will proceed on the floor to avoid "weaknesses in other components" that could create complications for the FHA director.
"There has to be a way to develop a bipartisan consensus on the GSEs and other pieces that Carol needs to have implemented and to do it all at once and do it the right way," he said.
The Senate is tackling the FHA overhaul first and intends to move quickly to a broader housing bill that overhauls Fannie and Freddie as part of a goal to reduce the government's role in the mortgage market.
Galante urged lawmakers to make sure they have an "understanding of the FHA's role in the larger housing finance system" as part of the broader overhaul.
Corker has joined with Democrat Mark Warner (Va.) on the bipartisan legislation to overhaul Fannie and Freddie, which is expected to come up fro consideration in September. There are other housing plans expected to emerge on both sides of the Capitol within the next couple of months, too.
The House, on the other hand, has combined all of the elements into one measure. The House Financial Services Committee approved a GOP-crafted measure earlier Wednesday that would eliminate Fannie and Freddie within five years and sharply curtail the government's role in the mortgage market.
The plan was approved without Democratic support. Two Republicans also opposed the measure.
Galante said on Wednesday that she is supportive of the bipartisan FHA overhaul bill hashed out between Senate Banking Chairman Tim Johnson (D-S.D.) and ranking member Mike Crapo (R-Idaho).
Overall, the measure would be helpful to ensure that the agency rebuilds its capital reserves and holds lenders accountable going forward, she said.
She cautioned lawmakers to avoid putting too many constraints on who can obtain loans from FHA. The agency's mission, she said, is to serve lower-income borrowers who need lower down payments while considering a broader range of factors in their ability to repay a loan.
"I don't think this bill damages our ability to do that so I support the changes requested here."
The House's bill would make FHA a self-sustaining agency outside of the jurisdiction of the Housing and Urban Development Department.
Galante told the committee that the agency, which struggled through the economic downturn, is continuing to see its balance sheets move on a positive trajectory with the number of delinquent loans dropping more than 15 percent during the past 18 months.
Rising home prices and an improving economy have put a positive spin on the agency's future finances.
She said the agency has already taken many steps to increase capital, including five premium increases, along with making major changes in loss mitigation and vastly improving its recoveries rates.
"We're moving in the right direction," Galante said.
She called the Johnson-Crapo bill's 3 percent capital requirement "a reasonable thing we can do" acknowledging that the previous 2 percent level was really only a cushion for a mild or moderate recession.
In addition, the agency's loan limits, which were expanded by Congress during the economic downturn, are set to expire at the end of the fiscal year, which is Sept. 30.
She told Sen. Joe Manchin (D-W.Va.) that she didn't consider the high loan amounts — upward of $729,000 — "troublesome" because those loans were not "particularly problematic" and it fulfilled the counter-cyclical role of the agency to take up the slack across nearly the entire loan spectrum when the economy nearly collapsed.
"I fully expect those higher loan limits to expire end of this fiscal year," she said.
"We should dial back and play a more traditional role."
Galante also urged lawmakers to examine more closely the agency's need to make technological improvements — their computer framework dates back to the 1970s — and to ensure the agency has the right staff in place to fulfill the aim of any legislation.
"I don't want to continue to whine about money and systems," she said.
"But it's very important in the future to have these kinds of systematic tools so we have the strength to analyze our portfolios."