Banbury's Horton General has been trying "very hard" since April to recruit new obstetricians.
But Victoria Prentis, Banbury MP, said the "contingency" midwife plan, which she is to discuss with health secretary Jeremy Hunt, was "terrifying".
Campaigners staged a rally earlier against the changes.
"Our bottom line in Banbury is we want our maternity unit to be the best it can be," Mrs Prentis said.
Oxford University Hospitals NHS Foundation Trust has told Horton staff the plan could take effect from the end of September if it did not successfully recruit the obstetricians, who are specially-trained maternity doctors.
Paul Brennan, director of clinical services, said the Oxford trust was trying "very hard" to fill the posts, which have been advertised since April.
He described the changes as "contingency arrangements in case recruitment continues to prove unsuccessful".
But Sophie Hammond, who was among campaigners at the rally, said "lives would be put at risk".
"The thought that these key consultants and this access to emergency care and surgery could be taken away from here doesn't bear thinking about," she said.
Mr Brennan said they had worked to make the obstetrician posts "more attractive to applicants".
"This includes enhanced pay and additional training at the John Radcliffe Hospital," he explained.
"We believe we have got a good offer for doctors wanting a role that offers some responsibility and also some variety, and are again re-advertising the posts."
According to the trust, women who do not want to give birth at the unit will be offered alternatives at other hospitals.
A decision is expected in late August.

Northumbria Police said the pair were arrested on suspicion of possessing indecent images.
A spokesman said investigations were ongoing to "ensure the safeguarding of those involved" and to check that there was no ongoing risk of exploitation.
Both boys have been bailed pending further inquiries.
Supt Sarah Pitt said the force was working with schools across South Tyneside to make children "aware of the risks around sharing images of themselves and others via text and social network sites".
She said: "The internet is an essential tool and social networking sites are a popular way for children to communicate with their friends, but we need to make sure they stay safe online and know how to use it responsibly.
"It's very important that we make sure young people stay safe online and are aware of the risks and what they can do to avoid them.
"Anyone who may have concerns about images they have shared or received should speak with a trusted adult or the police straight away."

Anna Jacobs read the description by Tecomak Environmental Services in an email inviting her for interview.
Attached seemingly by accident, the comments suggested Ms Jacobs, of Horsmonden in Kent, was "worth an interview if only for a laugh".
The company said it was investigating thoroughly but added the comments had been taken out of context.
Ms Jacobs told BBC South East Today she was initially excited to be invited for the interview for a position of office administrator.
But then she saw the "absolutely awful summary" and said she was "furious".
Below the formal invitation, the e-mail from Tecomak read: "Home educated oddball. Can't get a job since leaving uni. Forages for mushrooms.
"Difficult to assess from her CV - might be very good but equally could be a biscuit short of a packet or a left-wing loon tree hugger.
"Worth an interview if only for a laugh."
Ms Jacobs said she had a lot to offer and could not believe the firm was considering wasting her time for "a laugh".
So far, she said she has received no apology or explanation from Tecomak.
Employment lawyer Richard Atkins, said all jobseekers are entitled to equal treatment when applying for positions.
"On the face of it, this e-mail does not show that she has been treated with fairness and respect," he said.
A hospital's maternity services may become midwife-led because it is struggling to recruit doctors, an NHS trust has admitted.
[NEXT_CONCEPT]
Two schoolboys aged 12 and 13 have been arrested after concerns were raised about children sharing inappropriate images on social media.
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A graduate jobseeker has spoken of her horror at being called a "home-educated oddball" by a prospective employer.