The statement mirrored one issued March 15 for the same bill.
The veto threat marks the latest from the White House, as House Republicans have pushed to dismantle the administration's housing relief programs, calling them wasteful and ineffective.
HAMP in particular has failed to meet original expectations for the program. Designed to help 3 million to 4 million struggling homeowners modify their mortgages, the programs thus far has created just over 600,000 modifications.
The House GOP is pushing a package of four bills, which each would eliminate one housing program. The administration has threatened to veto each of them.
House Democrats have fought the bills. In a letter sent to Treasury Secretary Timothy Geithner, 50 Democrats called on the administration to fix HAMP, strongly opposing the Republican efforts to shutter it.