Perhaps no bill has garnered as much attention since the legislative session ended last month than the one requiring all children in public elementary and middle schools participate in at least 150 minutes of physical activity a week.

Now the question is: Will Gov. Bob Mc­Don­nell (R) sign, amend or veto the bill?

McDonnell has until Tuesday to make the decision, and he’s been lobbied by dozens of health and school groups.

Robley S. Jones, director of government affairs for the Virginia Education Association which opposes the bill, said, the governor is really “struggling with it.”

Even Attorney General Ken Cuccinelli, who doesn’t typically weigh in on policy issues, has an opinion on this one.

“I tell you, if I were the governor, I’d veto it,’’ Cuccinelli said in an interview. “You bet.”

McDonnell’s staff has met with representatives of the VEA, school boards as well as heart and cancer associations as the governor mulls what to do.

Some possible amendments that could be considered: Change the bill to include recess as part of the 150 minutes, allow students to skip physical education on days when there is inclement weather or require the General Assembly to provide money for the program.

“Everything is on the table for discussion,’’ said Keenan Caldwell, government relations director for the American Cancer Society. “All those kinds of things could be worked out.”

If Mc­Don­nell vetoes the bill, it is unlikely the General Assembly has enough votes to override his veto.

Del. John M. O’Bannon III (R-Henrico), who introduced the bill in the House, said he did not know how the governor would act, but he was hopeful that Mc­Don­nell would sign the measure. “The cost of not doing this is more,’’ he said.

Legislators passed the bill to help fight the growing problem of childhood obesity. In 2008, state legislators passed a bill recommending 150 minutes of activity in schools, but most did not abide by the recommendation.

Some school district officials oppose the looming requirement saying it could extend the school day, lead to cuts in arts and music classes, or increase costs because additional teachers would be needed.

Jones said if Mc­Don­nell signs the bill the VEA would ask the General Assembly to provide money for the schools in future years. The bill does not go into effect until 2014. “Everyone agrees with the goal,’’ Jones said. “If it’s done right, it’s going to be expensive.”

But O’Bannon said additional money was not provided because any elementary or middle school teacher can teach physical education so schools will not have to hire new teachers.

Legislators also agreed to recommend - but not mandate - 150 minutes of weekly physical education for high schools.

“Let the localities figure this stuff out for themselves,’’ Cuccinelli said. “They’re not incompetent. Some people have a great concern about a particular topic--childhood obesity. It’s not a topic unworthy of some concern. But that doesn’t mean we should just to do this one-size-fits all mandate to ‘solve’ it. Let’s face it. If you really drill down into childhood obesity, a lot of it just comes down to how individuals live their lives. And decisions they make. Making them go out and take a P.E. class, and therefore constraining what the people who are charged with educating them academically have available to them to achieve that goal, is not good policy.’’