He was an MP at the time, also Treasurer. In that speech he was talking about the Labor Party as compared to the Liberal Party, (earnest political opponents in theory, Tweedledum and Tweedledee in the light of sobriety). He went on to become an undistinguished Prime Minister for a few years in the 1990's before losing in a landslide.
Umm... Okay, so I think I know that Paul Keating was an MP in Australia at one point, and that he said weird things publicly. That's all I got. The "rule you" or "run you" vs. "rule us"/"run us" is where I'm lost. Is he talking about political parties? Or, Britain and Australia? Or, you know, North Carolina vs. Alabama barbecue? Weet-bix vs. Wheaties?
Ah, Internets! It so happens I can: Thursday, 26 May 1988, about 3.30 in the afternoon, Mr Keating's final paragraph on p. 3114 of Hansard. That says 'a gutser', but it's been edited at least to the extent of adding explanations in brackets that Keating wouldn't have said.
Where you all come aguster is, over here we think we're born to rule you. And let me tell you this, it's been ingrained in me from childhood, I think my mission in life is to run you.
— Paul Keating
Almost all hits for "come aguster" on the Web are this Keating quote; and there are only a few for "come a guster". The original expression is "come a gutser". It's not clear from this what Keating originally said, and whether 'guster' is a genuine variant or a spreading typo meme.