I honestly can't imagine why Republicans think the Chicago strike will hurt Obama, unless they think Chicago teachers — seriously pissed off by Rahm Emanuel and Arne Duncan — will stay home rather than go out and vote for Obama. Well, it's true that a lot of Americans are assholes, and won't figure out that the Chicago teachers are fighting Democrats. Nobody supports the American Federation of Teachers anymore, in either party, despite the perennial efforts of AFT to support, mostly, Democrats.
The "school reform" movement currently being pushed by Republicans and Democrats alike reflects a corporatist philosophy in that it demands that schools be run like for-profit businesses (and increasingly by for-profit businesses running charter schools.) Rahm Emanuel's push to open more and more non-union charter schools is a direct attack on the Chicago Federation of Teachers. So is his refusal to agree to re-hire laid off veteran teachers when new positions become available. Replacing them with beginning teachers would save the school district a lot of money.
The main point of disagreement, though, appears to be the extent to which student test scores are used to evaluate teachers. The union is ready to agree to test scores counting for 25% of a teacher's rating, but not to the 40% value Emanuel demands. Teachers know how misleading test scores can be. The same teachers who "succeed" in raising test scores one year very well may "fail" the next. So much depends on the quality of the students assigned to their classes.
Just one or two "mainstreamed" special education students with emotional disabilities can disrupt a class often enough to slow progress for everybody. Some children can be absent for as much as a third of the total days of instruction. Families in poverty often change addresses — and their children change schools — with distressing regularity. Many children grow up in home environments that discourage homework and study.
More than anything else, student test scores in any teacher's class depend on the luck of the draw (or the favoritism shown by administrators who assign children to classes.) As the old saying goes, "You can't make a silk purse out of a horse's ass."