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Chatfield, appearing on "Fox & Friends Weekend" with a participant in a recent lockdown protest, called for the governor and lawmakers to create a new strategy for fighting the pandemic.
"We're asking our government to work together," Brown said. "We elected these people to represent us so we can have representation. And, we are at a point where we can't continue to be locked down. ... The information we are getting is very confusing. People are really suffering and it's time that we get back to work."
Hundreds of protesters, some of whom were armed, stormed Michigan's Capitol building Thursday to voice their opposition to Whitmer's extended "stay-at-home" order.
Although protesters claim Whitmer overstepped her authority by temporarily banning most travel between homes, sales of items such as garden supplies and activities including some types of fishing, a state court ruled Wednesday that the constitutional rights of Michigan residents were not violated.
On Thursday, Whitmer extended Michigan's state of emergency and disaster declaration through May 28. As of Friday, the state had more than 41,000 confirmed coronavirus cases and nearly 4,000 deaths.
Chatfield criticized the governor for not working with the Republican-controlled state legislature.
"The law in Michigan is very clear," he said. "In order for any state of emergency to be extended, it requires an act of the legislature. orders and put those on her desk. ... We think that returning to the democratic process is an important step for us right now."
"We extended our hand to her in a partnership," he added. "She rejected that, and she decided to go it alone. ... The people of Michigan right now are frustrated. They've had their livelihoods taken away."
Chatfield told "Fox & Friends" host Pete Hegseth that he is considering filing a lawsuit challenging Whitmer's continuing lockdown.
"This [virus] is an unprecedented challenge, and we believe that it's going to require an unprecedented partnership, and that's what we're looking for right now," Chatfield said.
One of the lockdown protesters, Jodie Brown, said of Whitmer, "We really don't know what she is doing. I think that's why we gathered at the Capitol the other day -- because we need more definitive answers.
"And we are getting so many different messages from her -- what you can, what you can't, do. And they are ridiculous," Brown told Hegseth.
"We need people to understand that the citizens that gathered at the Capitol were there because they need their surgeries. They need people to realize ... the suicide rates are going up. We need to get back to our lives, and we're just so beyond frustrated," she said.
"This is really starting to take a toll on the emotional and mental health of the individuals in this state, and it's not fair," Brown added. "It's not fair that she ends up pushing up another 28 days."
"All of this is just out of control," she said.