The New Jersey governor and legislative leaders say they are working to repeal the travel bans in the states.
They say the governors intent was not to restrict travel to the US but to protect the US from terrorism.
But many of those who have travelled to the United States are concerned the travel restrictions will be implemented without sufficient oversight.
A spokesman for the New Jersey state Republican Party said the party would not support the executive order if it does not provide for adequate oversight.
He also said the ban should be enforced in an open and transparent manner, which has not been the case.
“This is a new era and we are moving forward with open minds and open hearts, and the governor and his allies in the Republican Party will have to come to grips with this new reality,” spokesman Mark Vercetti said.
The state legislature, which is controlled by Democrats, is debating whether to pass a law to repeal Trump’s order, which bans people from the seven Muslim-majority countries from entering the US.
Several Republican governors, including New Jersey’s Christie, have said the order is unconstitutional.
“We’ve had a president of the United State that’s bent on a total disregard for the rule of law,” New Jersey Gov.
Chris Christie said on CNN.
“He has broken every rule of the law.
I don’t think the president is fit to be the head of the federal government.”