The statement is based on a 2003 law Obama sponsored when he was an Illinois state senator. His bill expanded income eligibility for KidsCare and FamilyCare, the state health insurance programs low-income families. Both programs saw sizable increases in enrollment after the law was passed.
The Henry J. Kaiser Family Foundation looked at the Illinois program and found that the children's enrollment increased by 55,421 between 2003 and 2005, the year Illinois abolished an income requirement. Adult enrollment increased by 100,458 between 2003 and 2006. That comes to a total of 155,879.
Of course, it bears noting that expansion of health insurance was a big goal of the Democratic governor who signed the bill, and Obama's legislation had a co-sponsor, a Republican, in the Illinois House. But the simplicity of his claim is hard to dispute, and being able to work with others to achieve goals is a theme of the ad in which he makes the claim. It all ads up to true.