Shaun Bailey said he understood why people were "peed off" with Mr Johnson's leadership, which has been hit with a series of scandals over recent months surrounding partygate and disgraced MPs.
The West Bromwich West MP urged his party to "get our heads down and start delivering now" so people could see "some actual progress" on policies.
It comes as pressure mounted on the Prime Minister over the latest sleaze scandal, which saw Walsall-born Chris Pincher suspended as a Tory MP amid claims he drunkenly groped two men.
On a monthly Facebook live stream with constituents, Mr Bailey took a question on whether the PM "should go".
He said Mr Johnson remained the best man to lead the country, and warned it would be disastrous for Labour to regain his West Bromwich West seat, which was red for 45 years before he won it in 2019.
"I'm not saying Boris is perfect. I don't think he has been – and I think he would admit that," Mr Bailey said.
"But my honest view is that I don't look around at the moment and think there is someone there and I go 'yes, you'.
"And the truth of the matter is, this is a crap period of time, and you need someone in there who is over it, who is consistent and who gets what is going on."
He said it was important to "stick the course" even though some of the decisions had not been "perfect".
"And yes, it's been a bit of a mess," Mr Bailey added. "But locally, the truth of the matter is if we go back to Labour, then that's it."
Mr Bailey, who supported Mr Johnson in last month's confidence vote on his leadership, said it was time for the Government to start delivering.
"I understand why people are peed off. I'm peed off," he added.
"My view is I think we have got to get our heads down and start delivering now. We've got to see some sort of improvement in that situation.
"People are not expecting an overnight fix. But what people need to see, in my view, is the green shoots of something happening and some actual progress."
Meanwhile Downing Street has admitted the PM was aware of claims about Mr Pincher's conduct before appointing him as Tory deputy chief whip in February.