( CNN ) -- Nebraska lawmakers , meeting in emergency session this week , are set to change a controversial safe-haven law by sharply limiting the age at which a child can be dropped off with local authorities . Thirty-five children have been dropped off at Nebraska hospitals since the law was enacted . The state Senate voted 41 to 6 Wednesday to scrap the current version of the law -- which has no age limitation -- and instead establish a strict 30-day age limit . State legislators have expressed concern that , if the law is not changed , Nebraska 's social services system will be overwhelmed by older children delivered by parents from around the country who find they are unable to provide proper care . The legislature -- which has only one chamber , the Senate -- is expected to approve final passage of the revision this week before Nebraska Gov . Dave Heineman signs it on Friday . Nebraska 's safe haven law was intended to allow parents to hand over an infant anonymously to a hospital without being prosecuted . Of the 35 children who have been dropped off at hospitals since the law went into effect in September , however , not one has been an infant , officials say . All but six have been older than 10 , according to the Nebraska Department of Health and Human Services . `` The abandonment of these children -- and the harm it is causing them -- is an immediate concern , '' said Jen Rae Hein , communications director for the governor . `` Some children have been begging their parents or guardians not to leave , '' said social worker Courtney Anderson . `` They may not really understand why they are being left at the hospital . But they know they are being left , and the parent or guardian might be fleeing . '' On Tuesday , a 15-year-old girl was left at a hospital in Hall County , located in the central part of the state . Last week , a 14-year-old boy and his 17-year-old sister were dropped off at an Omaha hospital ; the girl ran away from the hospital . Earlier in the week , a father flew in from Miami , Florida , to leave his teenage son at a hospital , officials said . `` Please do n't bring your teenager to Nebraska , '' Heineman told parents in an interview with CNN . `` Think of what you are saying . You are saying you no longer support them . You no longer love them . '' State Sen. Tom White said lawmakers have been caught off guard by the number of teenagers dropped off under the law . `` What you 've seen is an extraordinary cry for help from people all across the country , '' he said . `` Nebraska ca n't afford to take care of all of them . Nebraska would like to be able to , but they know that we ca n't so we are going to have to change the law . '' Five of the 35 abandoned children were brought to Nebraska from out of state . Parents have traveled to Nebraska from Michigan , Indiana , Iowa , Florida and Georgia . `` We did n't think [ the law ] would be used to the extent it [ has been ] , '' state Sen. Brad Ashford said . `` We did n't anticipate children coming from other states . '' Tysheema Brown drove from Georgia to leave her teenage son at an Omaha hospital . `` Do not judge me as a parent . I love my son and my son knows that , '' Brown said . `` There is just no help . There has n't been any help . '' Safe-haven laws allow distraught parents who fear their children are in imminent danger to drop them off at hospitals without being charged with abandonment . Nebraska was the last state in the country to pass such a law . But every other state included an age limit . There are 6,600 children in state custody in Nebraska , according to the Department of Health and Human Services . The per capita rate is one of the highest in the country , said Todd Landry , director of the Division of Children and Family Services for the Department of Health and Human Services , . `` I think this has spurred some really healthy conversations about how do parents get the help that they need when they are struggling with some of these parenting issues , '' he said . `` And the message that we have been trying to get out is , 'Do n't wait until it 's a crisis . Reach out to your family and friends . ' `` CNN 's Ed Lavandera contributed to this report .
State legislature meeting to set maximum age for drop-off , rule out older kids . Social worker : `` Children have been begging their parents or guardians not to leave '' Mom : `` Do not judge me as a parent . I love my son '' Governor : `` Please do n't bring your teenager to Nebraska ''