Governor Mike Pence calls Indiana "the most veteran-friendly state" in the country.
The legislation would bar employers from discriminating against veterans.
Sen. Jim Banks authored the bill and says there is not enough information about why only half of veterans with post traumatic stress disorder seek help.
The federal government plans to reimburse Indiana for the half million dollars it paid to National Guard state employees during the shutdown.
The state says it has enough cash reserves to keep programs including the Women, Infants, and Children program.
Some of the employees who would be out of work were already furloughed earlier this year because of sequestration.
Staff Sergeant Randall Lane of Indianapolis died at Camp Phoenix on Friday.
The bill would create a tiered system for hiring federal employees that rewards National Guard members for their service even if they haven't deployed overseas.
Members of the Indiana National Guard are facing one day of furloughs per week between now and the end of September.
Col. Wayne Black is being promoted to become the Indiana National Guard's first African-American brigadier general.