The Obama administration’s main school improvement initiative has spurred education policy changes in states across the nation, but it is meeting with some last-minute resistance as the first deadline for applications arrives Tuesday.

Thousands of school districts in California, Ohio and other states have declined to participate, and teachers’ unions in Michigan, Minnesota and Florida have recommended that their local units not sign on to their states’ applications. Several rural states, including Montana, have said they will not apply, at least for now, partly because of the emphasis on charter schools, which would draw resources from small country schools.

And Gov. Rick Perry of Texas said last week that his state would not compete for the $700 million that the biggest states are eligible to win in the $4 billion program, known as Race to the Top, calling it an intrusion on states’ rights.

Still, about 40 states were rushing to complete applications for the Tuesday deadline, the first in the two-stage competition. The last-minute opposition is unlikely to derail efforts by most of those states to win some of the federal money.