PHOENIX — Facing a Tuesday deadline, the state House voted Wednesday to add another $40.6 million to programs designed to teach English to students who come to school speaking other languages.

 The 37-23 vote came amid grumbling by some that the state already is spending a lot of money on public education. Rep. Russell Pearce, R-Mesa, complained that most of the approximately 138,000 students classified as “English language learners’’ are either in this country illegally or, at the very least, here only because their parents entered the country illegally.

 That statistic is backed by research from the Pew Hispanic Center.

 But Rep. Peter Rios, D-Dudleyville, said most of the affected students are, in fact, U.S. citizens, even if their parents are not. And he said there is a legal obligation under federal law to ensure they have an opportunity to learn English. In the end, though, all but one of the Republicans voted to support the plan. Most Democrats were opposed, with several saying the measure provides nowhere near the amount of money really needed to properly teach English. “It’s a beginning,’’ said Rep. David Lujan, D-Phoenix. But he  figured it will take at least another $100 million — on top of this — for the state to meet its legal requirements.

 That issue, however, is likely to be fought out not at the Legislature but in federal court: Tim Hogan, who represents the parents who filed the lawsuit that resulted in the new funding, already has said wants U.S. District Court Judge Raner Collins to approve the money the state is appropriating. But Hogan said he will ask the judge to eventually order lawmakers to come up with more. Wednesday’s action comes as Arizona faces an April 15 deadline imposed by Collins for the state to at least provide these promised funds. That means not just approval by the Senate, where it now goes, but also the signature — or at least acquiescence - - of Gov. Janet Napolitano.

 Failure to meet the deadline means fines starting at $2 million a day, rising to $5 million daily after May 15. School districts now get an extra $365 a year for each student not proficient in English, a figure Collins has said does not meet the requirements of federal law. Adding $40.6 million would boost that $50.4 million spending by about 80 percent.

 But not all schools would get the same per pupil aid. That $40.6 million figure was based on a study by the Department of Education on the best method of teaching English. It concluded schools should provide four hours a day of “structured English immersion’’ to students, separate from other youngsters.

Schools then came up with figures of how much additional cash they need to teach to the “models,’’ with requests totaling nearly $275 million. But state School Superintendent Tom Horne pared those requests to $40.6 million, with some districts getting a lot more per pupil and some getting none.

 Lujan, a member of the Phoenix Union High School District governing board, said the dollars are nowhere near adequate to do the job. He said testimony in the lawsuit that is forcing lawmakers to act shows schools need at least an additional $1,000 per student.

 And he said the requirement to educate these students separately only adds to the cost.

 Lujan said if lawmakers aren’t going to provide adequate funds, they should at least divide up that $40.6 million equally and let schools decide how they want to teach English. That proposal, however, was rejected by the Republican-controlled Legislature.

 But House Majority Leader Tom Boone said the measure complies with the federal court order that the state determine what it takes to properly teach English and then fund it. In fact, Boone said, Collins’ latest order approves the teaching models. He said the only thing now left for the state to do to comply with Tuesday’s deadline is fund those models.

 And Rep. Mark Anderson, R-Mesa, said voters specifically directed in 2000 that the only acceptable method of teaching English is immersion — exactly what the models mandate. Even if Collins doesn’t demand the state spend more than that additional $40.6 million, that doesn’t end the lawsuit, first started in 1992.

 Attorneys for the Legislature are challenging the judge’s conclusion that they cannot force schools to use certain federal aid before qualifying for the extra cash this measure provides. If lawmakers win, that $40.6 million could be cut by more than half.

 And legislators still are contesting Collins’ ruling that schools are entitled to the additional funds for English immersion classes for just two years. The judge said there is evidence it takes some students longer than that to become proficient.