He told BBC Radio Lincolnshire: "It's got to be resolved. We're putting money in on a regular basis to keep the club going and we've told the Revenue we're not prepared to do that - it's not tenable.
"How can you continue to do that if there's no future of the club?"
Newton has asked supporters to write to the Revenue to show officials how important the club is to the local community.
He said: "If they wind the football club up it's of no benefit to them - they'll receive nothing. The football creditors will receive nothing. Boston will lose its football club.
"So far this season we've paid in the region of �200,000 in tax, national insurance and VAT that they've benefited from and they will lose that income stream.
If they wind the football club up it's of no benefit to them
David Newton
"By winding Boston United up it will not force the Football League to change their view on payment of football creditors so no-one is going to benefit by it," he added.
Boston entered into a Company Voluntary Arrangement at the end of last season whereby creditors would receive around half the money owed to them over the next three years.
The Pilgrims were relegated from the Football League last season, but further demoted to Blue Square North because the terms of the CVA went against football rules.
HM Revenue and Customs has a policy of not commenting on individual cases.
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