You are correct, ibut the analogy kind of falls down.
In approx 1435(don't quote me on the year) the Commons (as it was known then) argued in front of the Lords the Bishops and the Royals that since they were the ones who represented those who paid taxes, it was their sole power to levy taxes and authorise spending. (Edit: It wasn't so much as an 'argument' as a flat out demand otherwise the Commons would rise up and have their heads).
That is reflected in the current UK constitution, the American Constitution, the Canadian Constitution and ours. This is a principle that has been running unbroken for around 700 years.
The issue is that the upper chambers of the UK, the US and Canada were designed as aristocratic houses which weren't there to represent the taxpayer. They were there sort of as a ruling house institution.
That isn't particularly well reflected here where we set out from the beginning to create a state based upper chamber based on proportional representation. (The American Senate became this later on with direct election of Senators and we copied their second purpose as a state representative body).
Interestingly the House of Lords blocked Supply in 1909 which led to two general elections and the Parliament Act which significantly curbed the powers of the House of Lords.
The budget in question was Asquith's "People's budget." which introduced significant social welfare programs and taxes on the wealthy.
Had this had happened a hundred years prior, no doubt there would have been a war.
That is interesting. I believe that the House of Lords is not as powerful as it once was but still it is such a ridiculous institution to keep around.
The Senate in each system (except for the UK) has the ability to block or amend parts of the budget, if not supply entirely.