The chamber will reconvene again Friday morning to consider three additional amendments, including one that would wholesale replace the measure with a Democratic version, before holding a final vote on the entire bill.
The House rules committee will allow 44 of the 125 amendments filed to the GOP-backed rewrite of the No Child Left Behind Act to be debated Thursday.
There was never a doubt that the administration was going to threaten to veto this bill. The big question is whether lawmakers in the Senate can produce a bipartisan product that can actually get some support from Obama.
Republicans who don't think the House No Child Left Behind Act rewrite goes far enough in restoring education decisions to the states could gum up the works in floor debate.
Scratch beneath the surface of a White House analysis and it seems highly unlikely that the funding impact would be nearly as dire as the administration warns.
The bulk of the 125 amendments came from Democrats who are seeking to restore accountability and dedicated funding streams for certain education programs.
Making public schools work better is a "personal mission" for many governors, said Gov. Brian Sandoval, a Nevada Republican, at a National Governors Association meeting.
Duncan is worried about the impact of funding provisions, and a lack of investment in teacher quality, pre-kindergarten programs, and initiatives like Investing in Innovation.
The U.S. Secretary of Education is criticizing Republicans for not imposing limits on testing in the same breath he's calling for keeping annual, statewide assessments.
A new schedule would send the Republican-backed No Child Left Behind rewrite to the floor for debate Wednesday and Thursday, with a final vote scheduled for Friday morning.