McCarthy and Carey
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Led by actors Jenny McCarthy and Jim Carrey, they're marching against the medical establishment that says there's no evidence vaccines cause autism, CBS News medical correspondent Dr. Jon LaPook reports.

"We want to send the message to the CDC and our federal government that vaccinations schedules are not one size fits all for all children and that each child is different," said concerned parent Michael Williamson.

Their new battle cry: Spread out the vaccine schedule.

"Thirty-six vaccines in the first few years of the life are too many too soon," Carrey said.

By the time a child is two years old, the CDC recommends 14 different vaccines in as many as 28 doses. That may sound like a lot - but these shots have helped to wipe out diseases like smallpox, polio and measles, saving an estimated 33,000 lives a year, according to the CDC.

Even so, some are asking: Why give so many vaccines over a relatively short period of time? Dr. Paul Offit helped invent one of those vaccines.

"There is no advantage to spacing out, delaying or withholding vaccines," Offit said. "The only thing that will come of that kind of behavior will be allowing for a period of time to occur when children are at risk of vaccine preventable diseases."

The activists are also worried about the preservatives used to keep vaccines sterile.

Safety concerns about a mercury-based preservative called Thimerosol led to its removal from most childhood vaccines almost a decade ago. But since then autism rates have gone up, not down. Still, parents are asking lots of questions.

"I would say that as a pediatrician I spend about 50 percent of my day talking about vaccines," said Pediatric Dr. Bruce Brovender.

He insists his patients be vaccinated, but he's willing to compromise with parents - up to a point. Brovender warns them about the risks if they don't follow the schedule recommended by the CDC and American Academy of Pediatrics.

"They are 100 percent warned that by delaying or spacing them out they are not going to get the protection they need," Brovender said. "It's better to follow the academy's schedule, but it's better to get something than nothing."

He says the marchers have forgotten the consequences of failing to vaccinate properly.

"The child who didn't get the whooping cough vaccine and is now on a respirator and now may have permanent brain and lung damage," he said.