The administration has already made its mark on education through Race to the Top, a federal grant program in which 40 states are competing for $4 billion in education money included in last year’s federal stimulus bill. In his State of the Union address, Mr. Obama hailed the results so far of that competition, which has persuaded states from Rhode Island to California to make changes in their education laws. States that prohibit the use of test scores in teacher evaluations, for example, are not eligible for the funds. The competition has also encouraged states to open the door to more charter schools, which receive public money but are run by independent groups.

Now the administration hopes to apply similar conditions to the distribution of the billions of dollars that the Department of Education hands out to states and districts as part of its annual budget.

“They want to recast the law so that it is as close to Race to the Top as they can get it, making the money conditional on districts’ taking action to improve schools,” said Jack Jennings, president of the Center on Education Policy, who attended a recent meeting at which administration officials outlined their plans in broad strokes. “Right now most federal money goes out in formulas, so schools know how much they’ll get, and then use it to provide services for poor children. The department thinks that’s become too much of an entitlement. They want to upend that scheme by making states and districts pledge to take actions the administration considers reform, before they get the money.”

One section of the current Bush-era law has required states to certify that all teachers are highly qualified, based on their college coursework and state-issued credentials. In the Race to the Top competition, the administration has required participating states to develop the capability to evaluate teachers based on student test data, at least in part, and on whether teachers are successful in raising student achievement.

Educators who have talked to the administration said the officials appeared to be considering inserting similar provisions into the main education law, by requiring the use of student data in teacher evaluation systems as a condition for receiving federal education money. Mr. Duncan has publicly endorsed such an approach, Mr. Cunningham said.

The education law has been praised for focusing attention on achievement gaps, but it has also generated tremendous opposition, especially from educators, who contend that it sets impossible goals for students and schools and humiliates students and educators when they fall short. The law has, to date, labeled some 30,000 schools as “in need of improvement,” a euphemism for failing, but states and districts have done little to change them.

The last serious attempt to rewrite the law was in 2007. That effort collapsed, partly because teachers’ unions and other educator groups opposed an effort to incorporate merit pay provisions into a rewritten law. Earlier this month, Mr. Duncan and more than a dozen other administration officials took steps toward organizing a new rewrite, meeting with the Democratic chairmen and ranking Republican members of the education committees in both houses of Congress.