The MP for South-west Devon told Premier it was a "crazy" time for attempting to hold a leadership election.
He said he had confidence in Theresa May's Brexit deal once the issues around the back stop for the Northern Ireland/Republic of Ireland border have been tweaked.
His comments come as Theresa May vows to fight an effort to oust her as Conservative leader "with everything I've got".
In a dramatic early morning statement outside the door to 10 Downing Street, Mrs May warned a change of Prime Minister would put the UK's future at risk and could delay or halt Brexit.
She insisted she would stay on to "finish the job" she has set herself as Prime Minister.
Mrs May's statement came about an hour after it was confirmed the chairman of the Conservative backbench 1922 Committee, Sir Graham Brady, had received the 48 letters of no confidence from Tory MPs required to trigger a ballot on the leadership.
Speaking on Premier's News Hour, Streeter suggested the 48 letters which were needed to trigger the ballot represents a small fraction of Conservative MPs.
He said: "It's 15 per cent of the Conservative parliamentary party, which basically means that 85 per cent of did not want this challenge to happen.
"I think a substantial majority this evening will vote in her favour."
He said he hoped that progress on the back stop would be made at Thursday's European summit:"At that meeting, I am very hopeful that again progress will be made in enabling our colleagues who are concerned about this deal to vote for it and support it because the alternatives really are not in the national interest."
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