John McCain’s selection of Alaska Governor Sarah Palin as his running mate has made a huge difference in her home state.

McCain now leads his Democratic opponent nearly two-to one, 64% to 33%, according to a new Rasmussen Reports telephone survey of voters in the state. It is the first poll taken since Palin, who is extremely popular in Alaska, joined the GOP national ticket (crosstabs available for Premium Members).

In late July, the race was much closer in Alaska, traditionally one of the most Republican states in the country. McCain held a five-point lead over Obama.

But that poll also was taken one day after Ted Stevens, the state’s senior senator and the longest-serving Republican member of the U.S. Senate, had been indicted by federal authorities for allegedly hiding more than $250,000 in illegal gifts from an oil company.

McCain now has the support of 91% of the state’s GOP voters and 17% of Alaska Democrats. Obama is backed by 79% of Democrats and seven percent (7%) of Republicans. Unaffiliated voters prefer McCain by a 57% to 39% margin.

Nationally, while each candidate experienced a modest bounce after their conventions, the race is once again neck-and-neck, according to Rasmussen Reports daily Presidential Tracking Poll.

Seventy-one percent (71%) have a favorable opinion of the Republican nominee, including 40% who view him very favorably. In late July, only 24% had a Very Favorable view of McCain. Only 28% now see McCain unfavorably, and just 12% say their view of him is Very Unfavorable. Both these negative numbers are down.

For Obama, the opposite is true: His favorables are down, his unfavorables are up. The Democrat is regarded favorably by 45% of Alaska voters, with 25% saying their view of him is Very Favorable. But 55% have an unfavorable view of the Democrat, including 35% who say that view is Very Unfavorable.

Palin, the state’s first-term governor and now her party’s vice presidential nominee, is regarded at least somewhat favorably by 72% of Alaska voters, including 56% who say their view of her is Very Favorable. By comparison, 43% have at least a somewhat favorable opinion of Obama’s running mate, Senator Joseph Biden of Delaware, and just 18% view him very favorably.

Nationally, 56% have a favorable opinion of Palin and 53% say the same about Biden.

For 64% of Alaska voters, Palin was the right choice for McCain’s running mate, while just 33% think Obama picked the right person to run with him.

This perhaps explains why 83% of Alaska Republicans, as opposed to 73% of the state’s Democrats, say they will be voting with enthusiasm for their candidate come November. Only 19% of all Alaska voters say they will be voting primarily against the other candidate.

Lyndon B. Johnson in 1964 is the only Democratic presidential candidate who has ever won in Alaska since it became a state in 1959. George W. Bush carried the state by 25 points in 2004 and 31 points four years earlier.

For 36% of Alaska voters, economic issues are the most important in this election, while 29% rate national security as the priority.

Even in Alaska, just 43% say President Bush is doing a good or excellent job, but nearly as many (41%) rate his performance as poor.

Embattled Republican Senator Ted Stevens, now under federal indictment, has come back strong in his bid for re-election according to new polling released earlier today.

Rasmussen Reports also released new results from New Mexico and North Dakota today. Earlier this week, new presidential polling data for Colorado,Florida, Montana, Ohio, Pennsylvania and Virginia was made public.

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