* Teachers oppose evaluations tied to student performance
* Chicago's Democratic mayor has championed education reform
* Obama needs union support to win key swing states
CHICAGO, Sept 11 (Reuters) - Parents and thousands of Chicago children faced a second day of closed public schools on Tuesday as striking teachers and the nation's third-largest school district argued over details of education reforms sought by Mayor Rahm Emanuel.
Many parents stayed home from work with their children on the first day of a strike by 29,000 Chicago teachers and support staff Monday. But patience was likely to be tested on Tuesday as the largest U.S. teachers strike since 2006 dragged on.
The face-off in President Barack Obama's home city is the biggest private or public sector labor dispute in the United States in a year. The stakes are high for both supporters and foes of a national movement for radical reform of urban schools.
The Chicago dispute immediately became an issue in the U.S. presidential campaign with Republican candidate Mitt Romney criticizing Obama for his support of unions.
"I choose to side with the parents and students depending on public schools," Romney said in a statement on the same day he visited Chicago for campaign fundraising events.
Obama was careful not to get in the middle of the dispute between his former White House chief of staff, Emanuel, and a union that has supported Democrats with money and efforts to get out the vote in elections. White House spokesman Jay Carney said the president wanted the two sides to settle the matter quickly.
Since he became Chicago mayor in May 2011, Emanuel has championed education reform, successfully negotiating a longer school day for Chicago children. He wants teachers evaluated partly based on the performance of their students on standardized tests.
Chicago teachers fiercely oppose the proposed evaluation system, arguing that many of their students perform poorly on standardized tests because they come to school hungry and live in poor and crime-ridden neighborhoods. They also say that class sizes are too large to teach children effectively.
Police estimated as many as 10,000 teachers and supporters poured into the streets on Monday afternoon to protest Emanuel's school reform campaign.
Chicago Public Schools are offering teachers an average 16 percent pay rise over four years and sweetened benefits such as paid maternity leave and picking up most of the costs of pensions.
Representatives of the two sides met all day on Monday but failed to reach a deal. When Chicago School Board President David Vitale left the talks on Monday evening, he said the negotiators had not even discussed the vexing question of teacher evaluations.
"The union said they were not ready for discussion on those particular issues," Vitale said. "We want to get this resolved."
Chicago is offering some 350,000 children whose classes were suspended by the strike free meals and half day of supervision at facilities around the city.
The union had predicted chaos but there were few signs of problems at the centers other than frustrated parents.
Judy Poindexter, 70, picked up her granddaughter and two other children from one center at John D. Shoop Academy of Math, Science and Technology because their parents could not get off work.
"I support the teachers but I support the children even more, because the children need to be in school and they need to get their education," she said.
Antionette McCoy, 39, a restaurant manager, said she kept her two children, ages 12 and 14, who attend Beethoven Elementary School, at home on Monday because of concerns about safety.
She said she was angry at the school and teachers for not providing more notice and support to parents.
"I'm taking my kids back to a school in the suburbs," McCoy said at a nearby Starbucks. "I was considering staying because it was convenient. But I decided ... I had to get them a better education."