Rep. Carolyn Maloney (D-N.Y.) added that Cruz is someone who "refused to stand with New Yorkers in one of our hours of greatest need."

Cruz criticized the Hurricane Sandy relief package as "wasteful spending," and was one of 36 GOP senators who opposed the bill in January. Many Republican senators wanted to offset the cost of the bill, but the Senate rejected an amendment to do so in a 35-62 vote.

"I really do not believe that someone who thought the critical aid was quote 'wasteful spending,' which has already been too long delayed, would be invited by New York Republicans to talk at their state dinner," Maloney said.

Cruz's office told The Hill that Cruz supported a Sandy relief bill, but was opposed to legislation the Senate passed that included spending for items not related to Sandy relief. New York Republicans also rejected the Democrats' criticism.

"Senator Cruz is on record with his support for Sandy Aid," said Communications Director David Laska. "Carolyn Maloney and Hakeem Jeffries should be asking Harry ReidHarry ReidThe Memo: Trump pulls off a stone-cold stunner The Memo: Ending DACA a risky move for Trump Manchin pressed from both sides in reelection fight MORE why he wouldn't let a hurricane relief package reach the Senate floor without stuffing it full of unrelated pork spending."

Cruz will speak Wednesday night at the New York State Republican Party's fundraising dinner.

— This story was updated at 6:43 p.m.