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That has changed in the past couple of weeks as big national players became invested.

The Susan B. Anthony List, a pro-life group that has helped push 20-week bans in various states, has poured tens of thousands of dollars in advertising money into the initiative. President Obama’s political arm has become involved on the other side, using the vote to try to raise money.

“The groups behind the ballot initiative are extremely well-funded and — if they win in Albuquerque — you can bet they’re going to take this approach to cities and states across the country,” wrote Kaili Lambe, women’s issues campaign manager for Organizing for Action, the advocacy group that emerged from Mr. Obama’s campaign team.

New Mexico always has been liberal when it comes to abortion laws. It doesn’t restrict abortions late in the term, nor does it have parental consent, notification provisions, a waiting period, or any of the clinic safety restrictions that other states have imposed in recent years.

Mrs. Shaver said it’s called the Wild West of abortion, and she said that’s why Dr. Curtis has set up in New Mexico — and why he draws from so many other states.

Asked why New Mexico was different, Micaela Cadena, policy director for Young Women United in Albuquerque, said she views New Mexico as the constant and said it’s other states that have changed by adding abortion restrictions.

“It’s something about everywhere else in that those with an agenda have been able to restrict a woman’s access to health care decisions,” she said.

Uncharted territory

Both sides said it’s unclear how voter turnout will go and whether either side has an advantage in a special election like this one — particularly with no other big race on the ballot.

Early-voting turnout was running high.

“You look at our history and there’s nothing like it. There’s nothing outside of a presidential election that has this much interest,” said Julianna Koob of Planned Parenthood New Mexico. “This path that we’re going down is dangerous on a number of fronts and could happen anywhere in the country.”

Initial polling appeared to show the pro-life side winning, according to an Albuquerque Journal survey in September.

But a poll taken late last week sponsored by a blog, New Mexico Politics with Joe Monahan, showed opponents of the referendum winning 53 percent to 41 percent.

“The tide is not benefiting the pro-life movement as we near Election Day,” pollster Bruce Donisthorpe told the blog, adding that pro-choice voters probably have won the early voting and pro-life folks will have to make up ground Tuesday. “Those in favor of the ban are going to have to go outside the pool of regular, likely voters, to win this race and they don’t have a lot of time.”

It’s unclear exactly how many doctors in Albuquerque would be affected by the ban.

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