Recent TV and radio ads by opponents feature actor Martin Sheen, who calls the measure a "dangerous idea" that could be used by the most vulnerable in society. Supporters are on TV with an ad spotlighting a widow who says it lets those who are suffering have control over their final days.
With both sides having raised a combined $3.5 million, much of it still unspent, more ads are expected in the coming weeks.
The measure would allow physicians in Washington State to help terminally ill patients end their lives. Oregon, where voters first approved the idea in 1994, is the only state with such a law.
A recent poll by independent pollster Stuart Elway found that the measure was popular, with 57 percent of voters polled supporting it and 33 percent opposed. That poll, conducted in September, showed 10 percent still undecided, while 16 percent were leaning "yes" and 10 percent were leaning "no."
"It really is a matter of personal decisions and having the freedom to make your own decisions about end-of-life care," said Anne Martens, spokeswoman for Yes on I-1000.
Todd Donovan, political scientist at Western Washington University, said he wasn't surprised that Initiative 1000, also known as the "Washington Death with Dignity Initiative," is polling well.
"There is that libertarian streak in the northwest that it sort of taps into," he said.
The measure is strongly opposed by religious groups, and Catholic church officials said their opposition shouldn't surprise anyone.
"Our teaching has always been in favor of life," said Sister Sharon Park, executive director of the Washington State Catholic Conference. "The purpose of law is to protect, and this certainly does not protect the vulnerable."
Outside of Oregon, advocates of the idea haven't fared well. California, Michigan and Maine voters rejected the idea, and bills have failed in statehouses around the country. In Washington, voters rejected physician-assisted suicide in 1991.
This year's proposal differs in that it would not allow doctors to administer lethal drugs on behalf of patients who couldn't do so themselves.
Initiative 1000 mirrors the Oregon law, which took effect in 1997 after a lengthy court fight, and would allow the terminally ill to obtain lethal prescription drugs for ending their own lives.
Any patient requesting the fatal medication would have to make two oral requests, 15 days apart, and submit a written request witnessed by two people, including one person who is not a relative, heir, attending doctor, or connected with a health facility where the requester lives.
Critics say assisted suicide laws could exploit depressed or vulnerable people who worry they've become a burden on their families.
"This is not an issue of choice and keeping government out of end-of-life issues," said Chris Carlson, chairman of the Coalition Against Assisted Suicide. "It is a matter of injecting government more into end-of-life issues, and it raises serious questions about who will do the choosing."
Those who support I-1000 say it's a humane choice for those who feel they have no other option.
"The people who choose the law really want to live and have likely been through chemo or surgeries, and now it's to the point where they can no longer choose life," said Arline Hinckley, a social worker who has worked with terminally ill patients and is working with the Yes on I-1000 campaign. "I think the person who can't choose life should have the right to choose the kind of death they want."
Forty-nine people died under the terms of the law last year, according to a report by the Oregon Department of Human Services. Since it went into effect, more than 340 patients have used the law to end their lives.
Most suffered from cancer, and the most common end-of-life reasons they expressed were loss of autonomy, loss of dignity and a decreasing ability to participate in activities they enjoyed.
By Associated Press Writer Rachel La Corte