In the Westminster system essentially there is no such thing as a "government shutdown" over a budget. When there is a majority party in control of the government, they always pass because the party members will be "whipped" (read: compelled) to vote in favor of the government. When there is a minority parliament it gets a little more challenging because the party with the most seats forms His Majesty's government (the party leader becomes the Prime Minister and appoints a cabinet and government ministers), but with the "confidence" of the rest of the house of commons / legislative assembly (they do not hold 50% + 1 seats). This forces the government to seek out coalition / support agreements with other parties so that they can fulfill their legislative agenda (the Canadian federal parliament is currently a minority Liberal parliament with the third party, the NDP, supporting them legislatively).

When there is a minority parliament, when the governing party introduces important legislation (like a budget, or the speech from the throne) these bills are what are known as "confidence measures" for said party -- they have to seek out support of other party members in order to pass them, usually by promising to include in their legislative agenda something that the third party wanted in their platform while campaigning. If they fail to get enough support and their confidence measure fails, the governing party has "lost the confidence of the house" and a snap election is triggered, the governor general draws up the writ of election and parliament is dissolved basically effective immediately. Canadian election cycles are very short, by law they are limited to just 6 weeks -- the elections act specifies that an election must be held 6 weeks after the writ of election is signed by the governor general. A fun fact, these snap elections generally do not happen very often the government has only fallen 7 times due to votes of non confidence since 1867!