House Financial Services Committee Chairman Barney Frank (D-Mass.) on Thursday laid out a “grand approach” for getting a controversial measure to rescue at-risk homeowners signed into law by June.

He advocated bundling the measure, which many Republicans see as a government bailout of reckless borrowers, with other housing-related legislation the administration badly wants in order to swing support in favor of the broad package.

The large housing package Frank envisions has “a very good possibility” of being cobbled together next month and could be approved by the president in late May or June, he said.

The measure that is stirring controversy would expand the Federal Housing Administration (FHA) to allow struggling borrowers to refinance into more affordable, government-insured loans. Frank’s panel, which considered amendments to the plan on Thursday, is set to vote on legislation next week.

Frank said he learned on Monday that the administration would issue a “harsh” veto threat against the bill. But he nonetheless predicted it would become law as part of a large package of housing items, including one of the administration’s top priorities — reforming the oversight of mortgage giants Fannie Mae and Freddie Mac and the 12 federal home loan banks.

That measure would be grouped with two others — legislation to modernize the FHA  and one to raise the caps on mortgage revenue bonds issued by the states — that the administration supports. They would be moved together with the Frank foreclosure rescue plan and some housing tax items, such as a tax credit for first-time homebuyers and a measure to spur the development of affordable housing.

The package would not include legislation Frank’s committee approved on Wednesday to authorize $15 billion in grants and loans for states to buy and refurbish foreclosed properties. The White House has threatened to veto such legislation.

Frank predicted his strategy would overcome the opposition of some senators to heavy government intervention in the markets, including Richard Shelby (Ala.), the ranking Republican on the Banking Committee.  

“Given the kind of grand approach I’m talking about, I don’t think any one individual would be able to stop that,” Frank said.

He said that, like any chairman or ranking member, Shelby would be in a position to shape the package but that his influence would diminish “as the stakes get higher and as the package gets broader.”

The Bush administration and some prominent Republicans have softened their stance on using the government to help at-risk borrowers in recent months amid signs that the economy is worsening. The Republican nominee for president, Sen. John McCain (Ariz.), recently changed course on the matter and now backs a plan similar to Frank’s proposal.

After advocating more modest steps, the administration recently embraced the tenets of Frank’s plan to use the FHA to reach a broad group of borrowers, but stopped short of endorsing the legislation. It said it would pursue a similar plan on a smaller scale and without congressional action.

Frank said that he believed there had been an internal struggle within the administration over whether to back his proposal, arguing that his plan had some prominent proponents. “Ben Bernanke is for it,” he said.

In Thursday’s committee markup, the panel’s top Republican, Rep. Spencer Bachus (Ala.), warned in his opening remarks that the plan risks sending a message to people and financial institutions that “when they willingly take on excessive and ill-advised risks, the government will always ride to their rescue.”