On Thursday, Duke expressed nothing short of full confidence when she talked to reporters about Puerto Rico outside the White House.
Trump, who is expected to visit the island Tuesday with his wife Melania Trump, first wrote three tweets Saturday criticizing the "poor leadership" in Puerto Rico, saying local mayors "want everything to be done for them when it should be a community effort".
Hurricane Maria hit the U.S. territory more than a week ago, leaving it without power and its roughly 3.4 million residents short on fuel and other supplies.
On Sunday, however, she brushed off the criticism, saying that when patchy internet connections finally allowed her to see the president's tweets, "I smiled".
"The mayor of San Juan, who was very complimentary only a few days ago, has now been told by the Democrats that you must be nasty to Trump", the president alleged without any apparent evidence.
Following requests from Puerto Rico's governor, Trump on Thursday authorized that shipping restrictions, via the Jones Act, be waived immediately for the island over the next 10 days.
FEMA Administrator Brock Long piled onto the pushback against Cruz.
Cell phone service is spotty at best and you get the feeling the people who are suffering the most aren't sitting around watching the news to see what Donald Trump has to say. We have to thank every Puerto Rican man and woman, who for a long time, many of us didn't know Oscar Lopez Rivera.
Trump's latest missive could further inflame sentiment after he had earlier weighed in on the emerging fight over how to finance the already debt-stricken territory's recovery - comments that were viewed as premature and distasteful by some. Emphasizing the difficulty of the task of rebuilding devastated areas, Trump noted that the USA territory is "an island surrounded by water".
"We have done a great job with the nearly impossible situation in Puerto Rico".
The tweet offended some Puerto Ricans, but Rossello refused to criticise the president. She said even if she could book the tickets, there's no guarantee the flight will get out. "I don't know what world Trump is living in, " he said on CNN's "State of the Union'".
She continued: "If anybody out there is listening to us, we are dying, and you are killing us with the inefficiency and the bureaucracy". Cruz says that "if he asks to meet with me, of course I would meet with him".
He said he was not aware of Ms Duke's "good-news" remark.
"The people who are the best in this are the USA military".
San Juan Mayor Carmen Yulin Cruz is answering with her own tweets.
From there organizers will drop off the boxes to get shipped to Puerto Rico, Mexico and the Virgin Islands.