That bill is the Children's Hospital GME Support Reauthorization Act, H.R. 297, which would reauthorize grants for graduate medical education programs in children's hospitals. It's meant to help address what its supporters say is a shortage of pediatric doctors.

"Children in our communities are counting on this program to train a future generation of pediatricians," Pitts said last week. "This is a program with proven results and it is past time that we reauthorize CHGME and provide certainty to hospitals and doctors.

"The bill had overwhelming support in the last Congress, and we hope that this year the Senate will take it up and send it to the president."

A similar bill from Pitts was approved by the House in 2011 by a voice vote. Obama's fiscal year 2012 budget proposed the elimination of this program.

The House is also expected to pass H.R. 225, the National Pediatric Research Network Act. It would create a national pediatric research network consisting of research consortia that can receive grants from the National Institutes of Health.

Rep. Lois Capps (D-Calif.), the bill's sponsor, says its purpose is to spur research into children's diseases like spinal muscular atrophy, and help develop clinical trials to treat rare pediatric diseases.

A similar bill passed the House in 2012 by a voice vote.

Finally, the House is likely to pass H.R. 235, the Veteran Emergency Medical Technician Support Act. This bill gives grants to states that streamline the requirements veterans with a medical background must meet to become civilian emergency medical technicians.

The bill provides $1 million a year from 2014 to 2018 for these grants. The House approved a version of this bill last year by voice vote.