CHICAGO (CBS) — They might be the most unlikely of groups to say “No” to the mayor and get away with it: Chicago’s librarians.

Mayor Emanuel has backed off on a cost-cutting move to close libraries on Mondays, despite the library union’s refusal to make concessions.

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CBS 2 Chief Correspondent Jay Levine explains.

They’re a feisty bunch, these librarians, who held protests Monday to demand the Emanuel administration reinstate full hours on Mondays.

Monday morning, Veronica Bonilla found the doors to her neighborhood library locked. She left, disappointed.

“I used to bring the kids to the story time in the morning and they like it, so it’s going to be sad,” she said.

Earlier this month, the mayor ordered the libraries closed on Mondays, after the union refused to agree to work two half-days instead of one full day.

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Now, he’s relented, finding the money to do exactly what they want: rehiring nearly half the 176 employees who had been laid off.

Still not enough, they say.

“He has taken those steps. He seems to be realizing the importance of the libraries to the neighborhoods, and we’d like him to work with us to come the rest of the way,” says Anders Lindall, spokesman for the American Federation of State, County and Municipal Employees, Council 31.

The mayor says he will not restore all the cuts in library hours and jobs.

“They tried to make the libraries a bargaining chip for undoing the responsibility we had to bringing reforms to the rest of the budget,” Emanuel said. “And I’m not going to undo all the savings we achieved there and somehow try to hold the libraries hostage.”

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But so far, the librarians have succeeded in restoring most of the proposed cuts, probably because of the negative perceptions held by moms who bring toddlers to story time, students who use libraries after school and the unemployed who need computers to look for work.