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 education reforms sought by Mayor Rahm Emanuel.

"It's hard work," David Vitale, president of the Chicago Board of Education and lead negotiator for the city said of talks with the teachers union. "It's taking them ... more time than we think it should."

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 being tested on Tuesday as the largest U.S. teachers strike since 2006 dragged on.

"We're kind of winging it, to be honest," said Eve Ludwig, a parent outside one Chicago elementary school. "The kids stayed with their dad yesterday. Today they're with me. We're hopeful this will be resolved this week."

Chicago school officials said about 18,000 students took part in a half-day of "safe and engaging programming" on Monday at 144 public schools, supervised by principals, volunteers and non-union employees.

Three more schools will be open for half-day care on Tuesday, but will serve only a fraction of 350,000 students affected by the strike. Another 52,000 students at public-funded but non-union charter schools are attending classes as usual.

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 Monday as he visited Chicago for campaign fundraising events.

Obama was careful not to get in the middle of the row 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.

Randi Weingarten, president of the American Federation of Teachers, told CNN on Tuesday: "The president said, as he should, that this is a local dispute....This is going to be solved at the bargaining table between the mayor and the teachers union."

Since he became Chicago mayor in May 2011, Emanuel has championed education reform, successfully negotiating a longer school day for Chicago children. The way teachers are rehired to handle the additional hours is a key issue in the dispute.

Emanuel also wants teachers evaluated partly based on student performance on standardized tests, citing a new Illinois law mandating student performance as a measure for teachers.

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.

Teachers also say Emanuel has disrespected them since taking office and in bargaining talks which started last November, hardening attitudes and destroying any trust in the talks.

"What's happened in Chicago, as around the country," said Weingarten of teacher evaluations, "is that sometimes it's about who you know, not what you know, that actually keeps your job."

Emanuel has denied any disrespect.

"The system was designed by the teachers, for the teachers, and will be revised by the teachers," he told reporters on Monday. "Nothing could be more respectful of their voice and their role and profession."

Eric Wagner, a striking high school history teacher picketing with about 100 other teachers at Federico Gracia Lorca elementary school on Chicago's northwest side on Tuesday, said teachers stood united and firm "for a fair contract."

"It's amazing that Romney and Ryan have come out in support of Rahm Emanuel," he said, as passing cars honked horns in support of the picketing teachers. "Rahm has more in common with Mitt Romney than he has with the citizens of Chicago."

POLITICAL STAKES HIGH

Police estimated that as many as 10,000 teachers and supporters poured into downtown streets on Monday afternoon to protest Emanuel's school reform campaign. Picketing teachers said another rally was scheduled for Tuesday afternoon.

The strike represents a political challenge for Obama.

"The unions are a strong part of the Democratic party and when you alienate the unions you begin to pull the Democratic dominance of Chicago apart," said Dick Simpson, a political science professor at the University of Illinois at Chicago.

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, which critics say already gives the union too much.

"Don't Cave, Mr Mayor," said the lead editorial in the Chicago Tribune on Tuesday. "The CTU doesn't like to talk about those long waiting lists at charter schools. Nor is the union willing to recognize financial reality."

Talks were expected to resume on Tuesday. When 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."

Antionette McCoy, 39, a restaurant manager, kept her two children, ages 12 and 14, who attend Beethoven Elementary School, at home on Monday because of concerns about safety.

"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."