Massachusetts is having trouble finding affordable health coverage for part of its new universal health coverage program.

The Connector board, the agency in charge of setting up the program, has asked for a new round of bids and permitted carriers to offer programs without prescription drug benefits as well as programs with drug benefits.

A new Massachusetts law is supposed to push all state residents to get free coverage through government programs or subsidized or market-rate health coverage from private insurers on a guaranteed issue basis.

Residents earning at least 300% of the federal poverty level would have to have “minimum creditable coverage.”

Current plans call for deductibles for that coverage to be as high as $2,000 for individuals and $4,000 for families, but the plans could not impose annual or lifetime spending limits, and the products could not include an annual maximum, lifetime maximum or maximum benefit per illness or injury, officials say.

Originally, the products also could not exclude coverage for prescription drugs.

The Massachusetts Association of Health Plans, Boston, urged the Connector board to take a more flexible approach toward drug coverage, noting that many consumers and employers have bought plans that do not provide drug coverage.

The Foundation for Taxpayer and Consumer Rights, Santa Monica, Calif., says Massachusetts should push down program costs by forcing health care providers, health insurers and health maintenance organizations to justify their prices rather than by watering down program benefits.