The Virginia Autism Project is stepping up its efforts to lobby Gov. Robert F. Mc­Don­nell to sign into law the recently passed measure that would require insurers to provide some insurance for autistic children. The governor has until Tuesday to act.

Pat DiBari, the group’s president, said the group is working harder to get the governor’s ear amid rumors that the he is considering offering amendments that would further restrict the coverage.

“We strongly suspect he’s going to amend the bill. It’s just the chatter,” DiBari said, adding that he does not know specifically what the amendments would be.

The group is sending e-mails, letters and making telephone calls. In an open letter last month, DiBari, the group’s president, asked that McDonnell (R) enact the legislation without amendments.

“This legislation is the most restrictive and narrowly crafted in the United States, and any amendments, which may be suggested to you, are clearly attempts to diminish the bill further or defeat it,” DiBari writes in the letter. “This is a very reasonable and inexpensive bill, especially compared to the benefits it provides to the Commonwealth.”

The letter goes on to remind the governor of the rationale for the bill: that one of every 110 children has been diagnosed with an autism spectrum disorder, including one in 70 boys, and that failing to act would mean passing on the costs of treatments to schools, families and, ultimately, the state, when it becomes necessary to assist untreated adults with autism. DiBari says the governor’s office has not responded or even acknowledged the letter’s receipt. “We’re not getting access to talk to the governor’s office,” DiBari said.

Following 11 years of work by a grass-roots organization that took root in Northern Virginia, the Virginia General Assembly agreed to require insurers to provide autism coverage for children ages 2 to 6 with a benefit cap of $35,000. Business groups have fought the bill, saying the new mandate could contribute to pushing them out of the health-care insurance market.

The governor has not reached a decision on the bill, according to spokesman Tucker Martin, who also said he could not comment on whether the governor might amend the measure.