Emanuel canceled his appearance at an upcoming fundraising event sponsored by House Majority PAC, Democrats' Congressional super-PAC, Bowen added.

On Monday, Mitt Romney tied Obama to the strike saying he was "disappointed" with the union's decision to strike and it was clear that the president sided with the teachers.

Illinois Republican Party Chairman Pat Brady also said Monday that Emanuel should step down from his fundraising job to focus on local issues.

"Mayor Emanuel should put aside his Obama super-PAC fundraising work and put Chicago issues first," Brady said in a statement. 

—This story was updated at 2:25 p.m.