Illinois government offices remained open Saturday as the home state of former President Barack Obama commemorated his birthday under a new state law. The bill marking Aug. 4 as “Barack Obama Day” throughout the state was enacted without making the date a full-scale holiday. The Illinois House narrowly rejected a plan to make Obama’s birthday a state holiday amid worries that the cash-strapped state could not afford to give state state employees another paid day off.Obama turned 57. The law hailed Obama’s efforts to protect the rights of Americans and build “bridges across communities.”