Ludlow Councillor Darren Childs issued the challenge after NHS Shropshire, Telford and Wrekin declared a critical incident on Friday because of the "continued and unprecedented pressure on its services".
One MP has so far said she would be very happy to spend time alongside NHS staff, but another says he believes it could be a "distraction to the NHS staff."
Heath and social care chiefs said the most recent 'critical incident' had been caused by "relatively high numbers of patients in hospital and community beds with Covid-19", a high level of staff sickness, and a high number of people attending hospitals.
Councillor Childs, who was elected on his campaigning ticket earlier this year, said: "Once they see for themselves these challenges the service faces then we expect them to take action and demand they do something about this crisis.
"The crisis is now, people are dying in Shropshire Telford and Wrekin waiting for ambulances that are tied up at A&E.
"We need immediate funding into social care to free up beds and return the flow through the hospitals."
He added that "we've heard enough excuses and waffle from the people who are accountable and now we need them to take action."
Ms Morgan's commitment was welcomed by Shropshire Needs Ambulances and Shropshire, Telford and Wrekin Defend Our NHS.
Both organisations are working for investment in the care system to deal with bed blocking and delayed discharges which keep ambulances stuck outside hospitals.
Councillor Childs began campaigning for better ambulance response times after his baby daughter Myla suffered a seizure scare and faced a long wait for paramedics.
His story was featured on the Tonight programme on ITV1 in an episode entitled ‘999 National Emergency.’ He was filmed at his Ludlow home for the programme, which featured the problems ambulance services are facing nationwide.
Since he was elected to the council, Mr Childs has campaigned to improve ambulance response times and health services across the county. He also petitioned to return the Ludlow ambulance hub to the town after it was axed, along with a number of others.
One of the county's MPs says she would be "very happy to spend a shift alongside our hardworking staff in A&E but what our doctors and nurses really need is action from the Government to reduce the pressure."
North Shropshire Liberal Democrat Helen Morgan added: "This means more doctors, nurses, carers and capacity across health and care to stop the system-wide backlog which culminates in queues of already-delayed ambulances outside A&E.
“The staff aren’t to blame for this, the Government’s incompetence is.
“I’ve repeatedly urged ministers to take this situation seriously but as NHS and care staff work harder than ever before, the Conservative Government is on holiday.”
Shrewsbury and Atcham MP Daniel Kawczynski said he "supports the hard-working staff in the NHS" but believes that spending 24 hours in A&E "may prove to be a distraction to the NHS staff working there".
He also believes that unwell patients should not have people around them who are not members of the clinical team looking after them.
He said: "Part of addressing the difficulties experienced in emergency care in Shropshire is the modernisation of facilities at the Royal Shrewsbury Hospital."
To support this modernisation Mr Kawczynski, in conjunction with other MPs from Shropshire, "secured £312 million to support the Hospitals Transformation Programme, previously known as Future Fit".
He added: "In reply to a question in parliament in the House of Commons, the Deputy Prime Minister indicated that building work in the programme would commence in 2023. "
He has also asked a Parliamentary Question about a county-based ambulance service based in Shropshire rather than one run from Birmingham.
Councillor Childs' call comes the day before a predicted failure of the West Midlands Ambulance Service.
Director of nursing Mark Docherty predicted the service would likely fail around August 17 due to ambulance handover delays affecting response times.
It was described as a "catastrophic situation" with deaths happening "which should not be happening" as a result of patients not being transferred quick enough.
But now it has been confirmed the service will continue despite the pressing challenges with work under way to look at new solutions to tackle the issue.
A spokesperson for the West Midlands Ambulance Service said: "The ambulance service relies on each part of the health and social care system working together so that our ambulances can get to patients in the community quickly.
"Sadly, the pressures we are seeing in health and social care lead to long hospital handover delays with our crews left caring for patients that need admitting to hospital rather than responding to the next call. The result is that our crews are delayed reaching patients.
"We are working incredibly hard with all of our NHS and social care partners to prevent these delays, looking at new ways to safely hand over patients quickly so that our crews can respond more rapidly and save more lives.
“Whilst the service is under very considerable pressure the staff in our control rooms and our operational ambulances are working flat out to reach patients as quickly as possible. The service will continue despite these challenges."