He is battling to retain the role he has held since his surprise win in 2017, when he narrowly beat a Labour candidate.
And the 60-year-old said: "If we win then the message would be it's not inevitable that Starmer is going to be Prime Minister.
"If Keir Starmer can't win here it would put a huge question mark over the outcome of the general election, which parts of the media seem very certain about but voters might yet have an opinion on."
Sir Keir chose Dudley in the West Midlands for the national launch of his local election campaign, suggesting he has high hopes of unseating Mr Street.
Council elections are taking place on the same day and Labour also hopes to gain control of the Conservative-led local authority, providing a springboard in the race for No10.
Dudley, like much of the West Midlands, contains a number of marginal seats that the Tories took from Labour in the 2005 and 2010 general elections, and Sir Keir now hopes to regain.
Mr Street said: "This is a very high-profile campaign for the Labour Party nationally.
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