Republicans have stressed that no taxpayer money would be used to bail out Puerto Rico from a crisis that has left nearly half of the population in poverty amid closings of schools and hospitals and a contracting economy.
During a Rules panel debate that stretched into the night, the committee rejected pleas to allow amendments that would have changed the basic structure of the legislation and the operation of the oversight board.
If the bill passes the House, action would move to the Senate, where some leading Democrats have said they would seek significant changes.
Earlier on Wednesday, House Natural Resources Committee Chairman Rob Bishop, who ushered the bill through his committee on May 25, told reporters he expected the full House to pass it on Thursday.
Bishop, a Utah Republican, said a strong vote for passage in the House would help propel it through the Senate.
"The bottom line is the better the vote here (in the House), the less likely it's going to come back in a significantly altered form" from the Senate, Bishop said.
Supporters hope to get it enacted into law before July 1, when Puerto Rico faces a deadline for making a $1.9 billion debt payment that it might not be able to fulfill.
The House Rules Committee voted to allow debate on a limited number of amendments, including one giving priority to protecting federal taxpayer investments in Puerto Rico, such as mass transportation assets.
Another amendment expected to be debated would expand a federal program aimed at encouraging economic development in Puerto Rico's "under-utilized" business zones.
Representative Raul Grijalva, a senior Democrat who worked on the bill, said Puerto Rico's debt crisis, if unaddressed, could grow into a humanitarian crisis. Stabilization measures contained in the bill, he said, "would be the first step toward getting the situation under control."
But his fellow Democrat, Puerto Rican-born Representative Luis Gutierrez, warned, "I don't think many of my colleagues in this body appreciate just how deeply offensive the bill before us is regarded in Puerto Rico."
He was particularly concerned with the way control board members would be chosen, with most not having to have any ties to the island.
But Gutierrez failed to convince the committee to allow amendments to be offered making changes to the board and its operations.