The police minister has agreed to hold further talks about giving Lincolnshire Police more money. Police officials said the force was one of the lowest-funded nationally. It expects to overspend by �7m next year.
Senior officers have warned average council tax bills could rise by up to �100 per year if it does not get an increase in funding.
John Hayes, Conservative MP for South Holland and the Deepings, met Tony McNulty MP for discussions on Tuesday.
It is hoped further discussions will be held within the next few weeks and involve all of the county's MPs.
Mr Hayes said: "The Police Authority have said that this could mean cutting 364 members of police staff.
"In an establishment of something like 1163 that would, in their words, be perilous. It could mean the closure of police stations, it could mean less officers on the beat. We already have a big problem in our rural area."
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