Early returns Tuesday night showed the charter schools measure, Initiative 1240, passing narrowly statewide - but behind in voter-rich King County.
The supermajority proposal, Initiative 1185, passed decisively throughout the state.
Anti-tax crusader Tim Eyman cited the results as he called on the Legislature to amend the constitution to make the two-thirds requirement permanent. Initiatives requiring a supermajority for tax increases have repeatedly passed in the state.
"We're not asking for a handout. We've earned it," Eyman said after the first vote tallies were posted online. "We really think this is a clear and unambiguous message from voters."
To amend the state constitution, the Legislature would need to pass the amendment with a two-thirds majority of both houses. The measure would then require a simple majority vote of the people.
Charter school measures have been less popular in Washington state, where voters have rejected the idea three times - in 1995, 2000 and 2004. Washington is one of just nine states that do not allow the independent schools.
Gordon Ross of Bellevue thinks Washington should give charters a try.
"I'm from California, and charter schools work. They're a good alternative," said Ross, 58, who moved to Washington two years ago.
Supporters say the charter school proposal would open as many as 40 of the independent schools over five years and would offer hope for struggling kids and their families. Opponents say charters have a mixed track record in other states and they would take away money from regular public schools.
Jerilyn Fowler of Seattle said she voted against the charter initiative because she was worried about the impact on traditional public schools.
"Schools need a lot of work," said Fowler, who attended private schools as a child.
Proponents of charter schools raised more than $10 million to promote the idea, including $3 million from Microsoft co-founder Bill Gates. Opponents raised considerably less, but had the vocal strength of teachers represented by the Washington Education Association behind them.
The two-thirds tax restriction, meanwhile, has been passed by Washington voters four times since the 1990s. Eyman took over sponsoring the initiative in 2007. He has since filed it every other year to deter lawmakers from suspending the rule, which they can do with a simple majority vote after two years.
Eyman's initiative was somewhat overshadowed this election season by a Washington Supreme Court case to decide the voting requirement's constitutionality. The court has yet to rule on that case.
The supermajority initiative was last approved in 2010 with 64 percent of the vote and appears to be winning with the same margin this year.