In a move that adds momentum to efforts to integrate immigrants, California is on the cusp of becoming the largest state in the nation to extend state-subsidized health care coverage to children from low-income families who are in the country illegally.

Democrats, immigration groups and health care advocates celebrated the announcement as both a cost-saving move and social progress for the state’s estimated 2.5 million immigrants who are in the country illegally. Critics, however, worry that the overburdened state-funded health program can’t handle another 170,000 children.

Gov. Jerry Brown and legislative leaders announced a $115.4 billion budget agreement that for the first time includes state funding to cover low-income children under 19 regardless of their legal status in Medi-Cal, the state’s health care program for the poor.