Mr Shapps also dismissed the mixed reception received by Mr Johnson as he attended a service at St Paul’s Cathedral on Friday, where boos could be heard from the crowd.
The Transport Secretary noted there were also cheers for the Prime Minister and said “politicians don’t expect to be popular all the time”, arguing “it’s best to get on with running the country “rather than being overly distracted” by the incident.
Asked if he believes there is going to be a vote of no confidence in Mr Johnson this week, Mr Shapps said: “No, I don’t actually, in the round when people judge Government by the general election, rather than mid-term where it’s not unusual to see polling like this, actually people make a decision about whether you’ve delivered and done a good for the country as a whole.
“I’m absolutely certain, with some of these huge decisions, sorting out Brexit, getting through coronavirus, seeing the largest growing economy last year, these are decisions and actions which will in the end matter to people.”
Asked if Mr Johnson would win a vote of confidence, the Transport Secretary said: “Yes, he will.”
Mr Shapps’ backing comes amid speculation Mr Johnson could face a crunch vote on his premiership as soon as this Wednesday amid reports the threshold for a no-confidence vote might have already been reached.
Meanwhile, new polling suggests the Conservatives risk losing a key electoral test later this month by a significant margin.
A survey of voters in the battleground constituency of Wakefield who will go to the polls on June 23 to elect a new MP has suggested the Tories could lose the by-election by as much as 20 points.
A by-election will be held on the same day in Tiverton and Honiton, which was called after Tory MP Neil Parish resigned over his viewing of pornography in the Commons.
Asked about the poll on BBC’s Sunday Morning programme, Mr Shapps said: “I think actually the best thing to do with all elections is to allow the people to speak and do so at the ballot box.
“You often get polls which show a variety of different situations.”
Asked if the Prime Minister will “be out” if the Conservatives lose both seats, Mr Shapps said: “No. Look … when it comes to a general election people look at Government and they look at it in the round, they look at what you’ve done.”
Under Conservative Party rules, if 54 letters of no confidence in Mr Johnson’s premiership are submitted to Sir Graham Brady, the chairman of the 1922 Committee of backbench Tories, then a leadership vote will be held.
The Sunday Times said it had been told as many as 67 letters had gone in which, if correct, would mean the threshold has been reached.
The rebels would need 180 voters to remove the Prime Minister.
Wakefield constituency polling by JL Partners and reported in The Sunday Times is putting Labour on 48 points compared with 28 points for the Conservatives – a 19-point slip on the winning Tory performance two-and-a-half years ago.
James Johnson, co-founder of JL Partners and a former Downing Street pollster during Theresa May’s tenure, said the so-called partygate saga looked to have damaged the Tory reputation among Red Wall voters.
The polling expert said the top reason swing voters in the West Yorkshire seat – who are voting for a candidate to succeed former Tory incumbent Imran Ahmad Khan after he was found guilty of sexually assaulting a boy – gave for preferring Labour was because “Boris Johnson tried to cover up partygate, and lied to the public”.