Maria, the most powerful storm to strike Puerto Rico in almost 90 years, has killed at least 16 people on the island.
The presenter of the video said the hospital she was in had "no water, no cash", and added that "the hospital is completely full with no generators, so they have open windows".
"I can not fathom the thought that the greatest nation in the world can not figure out logistics for a small island", said Ms Cruz. "If anybody out there is listening to us, we are dying, and you are killing us with the inefficiency".
The president is responding by citing what he calls "such poor leadership ability by the Mayor of San Juan, and others in Puerto Rico, who are not able to get their workers to help".
Customs and Border Protection spokesperson Gregory Moore said in a statement earlier this week, which came before Trump's waiver, that "the situation in Puerto Rico is much different" than it was when the storms hit Texas, Louisiana and Florida. "Right now, Puerto Rico needs all the help it can get".
He also suggested that Cruz had been told to criticize the president by "the Democrats" after earlier praising the relief efforts.
The decision to waive the flight policy for Puerto Rico may be why Trump claims he's received rave reviews for his administration's response to the tragedy in Puerto Rico, which is now struggling with a lack of drivers to move aid from ports to victims.
President Donald Trump says Washington is - in his words - "fully engaged in the disaster and the response and recovery effort".
"If mayors decided not to be apart of that [relief effort] then the response is fragmented", Long told Chris Wallace on "Fox News Sunday" in response to criticism from the mayor of San Juan, Carmen Yulin Cruz".
Hurricane Maria hit the island as a Category 4 storm back on September 20, which killed at least 16 people and left around 3.4 million residents without power and water.
Many of its 3.4 million residents have been without electricity, reliable drinking supplies and other basic necessities since the storm struck.