"No one would believe that Nicky Wagner set out to be offensive to people with disabilities," English said.
Little said he was "frankly stunned" by Wagner.
"It is just so at odds with the way she should be discharging her responsibility it, frankly, beggars belief."
Labour has previously criticised Wagner after she strongly criticised Idea Services over a contract dispute in April, saying the operational arm of IHC New Zealand had been "totally irresponsible" and let down vulnerable clients.
Little said those comments combined with the controversial tweet made it look like Wagner "doesn't really care about disability issues, like she's just going through the motions".
Wagner told the Herald she had made a silly tweet with "a slip of the finger" but explained she didn't mean she didn't want to be at her meetings.
"We just thought 'wouldn't it be good to have our meeting on the harbour?'.
"I was surprised [with the reaction] it was a very innocent tweet. It was a beautiful day outside and we were inside."
Wagner said she would not delete it out of fear that it would look worse. Otherwise she said she had a fantastic day meeting with the Murray Halberg Trust, the Equal Employment Opportunities Commissioner, the New Zealand Artificial Limb Service and EMA on disability issues.