Mr Davis was shadow home secretary and ran for the Tory leadership
Plans for fixed-term parliaments that could only be cut short if 55% of MPs voted to do so are a "serious mistake", says senior Tory MP David Davis.
The coalition deal would give the power to dissolve Parliament to MPs - but only if a "super majority" backed it.
The ex-shadow home secretary said it could mean a government supported by only 45% of MPs could not be removed.
Prime Minister David Cameron has pointed out that, in Scotland, 66% of MSPs must vote to dissolve Parliament.
He argues he is giving up a lot of power by introducing fixed-term parliaments - rather than deciding himself when to go to the Queen to ask for parliament to be dissolved, within a five-year term. Last week he said any fixed-term parliament required a "mechanism" to deliver it - but the details would be debated by MPs.
But Mr Davis, who ran against Mr Cameron for the Conservative leadership in 2005, said although people had repeatedly referred to Scotland - other countries with fixed-term parliaments required only a "simple majority" of MPs to dissolve parliaments.
"Austria, Belgium, France, Germany, Holland, Sweden all have fixed-term parliaments - they are complicated some of them, but all have a simple majority - none of them have super majority."
He said in Scotland there was a White Paper, manifestos and a referendum before the change was brought in.
He told BBC Radio 4's World at One programme: "I think it's a very serious mistake.
"The consequence in the extreme is you could have a government in parliament which could command 45%, or 45% plus one, of Parliamentary votes but no more and therefore couldn't deliver a Budget, couldn't deliver its manifesto, couldn't deliver its normal legislation and yet couldn't be thrown out either, because you can't force a dissolution."
"That is frankly a terrible formula for government, it could end up with a sort of crippled government."
The existing threshold for a no-confidence vote of 50% of MPs plus one will remain the same.
But while at present, if a government loses a confidence motion the usual practice would be for the PM to ask the Queen to dissolve parliament - with a fixed-term parliament he or she would no longer have the power to do so. Instead 55% of MPs would have to vote to do so.
The threshold would currently stop the Conservatives alone engineering a no-confidence vote - or the Lib Dems walking out on the coalition and siding with opposition MPs to force one.
He denied he was annoyed about not getting a job in the new coalition government and said he had "deliberately not talked to people" because he did not want to create problems for them.
But he said he thought "a very large number" of Conservative MPs were worried about the plans.
He said the issue was central to Parliament's ability to dismiss failing governments, adding: "We can dismiss failing MPs now, but ironically, MPs can't dismiss failing governments."
But Professor Gavin Phillipson, who teaches constitutional law at Durham University said a prime minister who lost a confidence motion would still have to resign.
"This won't stop MPs being able to bring down an unpopular government, just as they can now."
The 55% threshold was about a separate issue - when Parliament can be dissolved early, he said.
Currently, losing a confidence motion tended to lead to the prime minister asking the Queen to dissolve Parliament, triggering a general election.
But he said: "Under the proposed change, parliament would remain sitting and the political parties would have to see if they were able to form a new government - either a minority administration supported by a 'confidence and supply' agreement or a new coalition with a new prime minister.
"The idea behind the 55% rule is to make sure that one party on its own can't trigger a fresh general election."