I have a sister like that. Try a discussion where you both will agree only to talk about facts, not feelings. Discuss issues, not what you think of the individual politicians or spokespeople.
And have facts at your side. For example, tax cuts have always resulted in increases to the Nat'l treasury. That is not arguable, even if the Liberals "feel" that it can't be so.
My brother and I largely agree on economics. Indeed, on that score, if anything, I am a bit to the left of him. My bother likes to think of himself as a pre Goldwater liberal Pubbie, whose party long ago abandoned him, as the Southern Baptists and other suspect types took control. But when he saw the quarterly check I wrote to Uncle Sam this June, he noted that he understood better why I was a Bush supporter. I told him I thought in all good conscience, I should probably pay more. And so it goes.