Massie also objected to a bill temporarily extending the National Flood Insurance Program, which technically expires on Friday.
There was also language in the disaster bill to extend that authorization; it wasn't immediately clear if the flood program would be fixed in time, or if it would lapse at the end of the week.
Last Friday, it was Rep. Chip Roy (R-TX), who objected to House approval of changes made by the Senate to the disaster measure; Roy said a full roll call vote should be held, but with members gone this week back in their districts, that can't happen until early June.
Like last week, the objection drew scorn from some on the GOP side, whose states need disaster relief.
"This is yet another example of politicians putting their own self-interest ahead of the national interest," tweeted Sen. David Perdue (R-GA), who had interceded with President Trump on Thursday in order to salvage the disaster aid measure.
“Unfortunately, more clowns showed up today to once again delay disaster relief for the states and farmers devastated by the storms of 2018,” tweeted Rep. Austin Scott (R-GA).
Democrats also expressed frustration at the latest objection.
"Again, this was a bipartisan bill passed overwhelmingly by the Senate," said House Majority Leader Steny Hoyer (D-MD).
“The heartlessness of House Republicans knows no bounds,” said House Speaker Nancy Pelosi.
"Frankly, I cannot understand why any member would object to giving relief to so many millions of our citizens who have been badly damaged by natural disasters," Hoyer told reporters.
"We need action," said Rep. Debbie Mucarsel-Powell (D-FL).
But Republicans said this is about following regular order in the Congress.
House Republican leaders were not behind the objections, as they had signed off on the effort by Democrats to obtain quick approval of the disaster aid bill.