What happens to my car tax?

Short answer: you still pay taxes even if the monorail dies.

If the monorail is killed, Seattleites won't get their money back. In fact the tax would likely continue for two years to pay off debts. If the monorail is ultimately built, the tax will be levied for at least 25 years, likely longer.

The article also has a chart to estimate the cumulative taxes you might pay over the course of 30 years.