That would be 25 percent of the $500-per-child credit the Republicans have sought.
Republicans had sought last year to hold premiums at what was then their current level.
Republicans have long sought to give local government more control over federal money and the amendment is a small step in that direction.
This is a circumstance that Republicans are seeking to change.
Republicans had sought tighter rules and wanted to put all the measures before voters.
The Republicans are also seeking the promise of a floor vote for their bipartisan alternative.
Republicans have sought to reduce the $12 billion revenue figure, asking the Democrats to cut more spending instead.
The program emphasizes local control, and Republicans have often sought to consolidate other programs in a similar way.
The Republicans sought additional restrictions even though they hailed the program as passed last year.
Republicans were meeting among themselves and also seeking Democratic support for a resolution doing what the President asked.