* 41.1 million vaccines now out of the factories

* Sanofi CEO says production picking up

* CDC expert: U.S. could have managed expectations better

By Maggie Fox, Health and Science Editor

WASHINGTON, Nov 10 (Reuters) - The flow of swine flu vaccines to the U.S. market is picking up, health and corporate officials said on Tuesday, and now the challenge will be to get the drugs to people.

Dr. Anne Schuchat of the U.S. Centers for Disease Control and Prevention said 41.1 million doses of H1N1 vaccines are either available or have been delivered but that state and local health officials still face logistical problems.

"I can't tell you how many times in our outreach to our counterparts that we got messages back saying 'It's Friday, we are furloughed' or 'We are out today'," Schuchat told a Senate health subcommittee hearing.

Many U.S. states have furloughed workers -- making them take a day off without pay -- because of budgets hit by the recession.

"I think the key barrier to our immunization effort is really the fragility of the public health infrastructure," Schuchat said. "There have been about 15,000 jobs lost in that sector over the past two years."