Shrewsbury and Telford Hospital NHS Trust's board will meet this week and decide whether to go ahead with an overnight closure of the emergency department at Royal Shrewsbury Hospital or Telford's Princess Royal Hospital on safety grounds.
Gaps in consultants, middle grade doctors, the junior doctor workforce and nursing staff have been highlighted as concerns.
But Wrekin MP Mark Pritchard said that at a time of unprecedented demand for A&E services, both of the county's emergency departments need to be kept open.
He said: "Increasingly I meet constituents who are frustrated at the constant and running negative headlines about the hospital trust.
"Questions are now rightly being raised about whether the hospital trust has the right senior management in place and whether the governance structure of the local trust is fit for purpose."
Telford & Wrekin Council leader Shaun Davies said closing an A&E overnight would only be dealing with the symptoms and not the cause of the issues.
He says he is also concerned that if the emergency centre in Telford is closed overnight it could lead to children having to leave the county for treatment, and there would be fears that it may not fully reopen.
Councillor Davies, who claims it is not too late to put a rescue plan in place for the trust, added: "People will see it as a kick in the teeth."
He also claimed the trust has an issue of poor leadership, saying people deserve better.
Telford MP Lucy Allan said: "Throughout the uncertainty created by the Future Fit process we have been continually reassured that under any scenario both PRH and RSH will have 24-hour accident and urgent care.
"Government has provided record levels of new funding for a brand new emergency unit, for a new ward to alleviate winter pressures and to fund an extension to PRH A&E.
"So in this context, for the hospital trust to now say that night time A&E closures may be necessary because staff do not want to work for the trust, is an extraordinary admission of management failure.
"Why is it that clinical staff do not want to work for SaTH? Is it the reputational damage caused by the baby death scandal?
"Is it the management culture, the uncertainty, the dithering and delay when it comes to decision making as evidenced by Future Fit?
"What is clear is that these problems appear to be unique to this trust and our community is being failed.”
Former health minister and Ludlow MP Philip Dunne says the decision over any overnight A&E closure is for clinicians and those responsible for running the trust, and added that patient safety is paramount. He said: "It clearly would be very regrettable if either A&E was to close in a disorderly fashion.
"NHS leaders have been preparing contingency plans for some time so it doesn't come as a huge surprise but it's clearly indicative of the problems we've had in Shropshire for some time."
He said issues would be resolved through Future Fit and a decision is needed to end the problems.
Daniel Kawczynski, MP for Shrewsbury and Atcham, has agreed that it was imperative for a decision to be reached on Future Fit, which will decide the future of hospital services in the county.
SaTH's trust board will meet at Royal Shrewsbury Hospital on Thursday.