The Republican Party’s 2012 electoral juggernaut—and, make no mistake, it is a juggernaut—has decided to go “all in” on the fight for retired Congresswoman Gabrielle Gifford’s seat from her Democratic party.

The special election to fill the seat, which takes place Tuesday, has seen massive outside spending (by GOP groups and by “independent” allies such as Karl Rove and Dick Armey) on behalf of a Republican who hopes to grab it for his party. Democrats have fought back aggressively in the closing days because they know they cannot afford to lose the seat.

How should Americans who don’t happen to live in Arizona see this particular contest?

It’s best understood in the context of similar elections in Britain—where they are referred to as “by-elections.” When a by-election falls shortly before a general election, it is seen as something of a test run; or, at the very least, an indicator of where particular regions are trending.

That’s what Tuesday’s Arizona vote has become, with significance to the races for president and for control of Congress. And massive outside spending to emphasize the point.

All sides are taking it seriously, and rightly so. Southern Arizona’s 8th district is “swing” territory, with a slight Republican lean but more than enough independents to tip it Democratic when the party (or a particular candidate) is running strong.

So it’s a significant testing ground for 2012 politics. And not just Congressional politics.

Southeast Arizona, especially the Tucson area, will be a critical base for President Obama if he hopes to win the state in November.

The Obama team has long entertained a Southwestern strategy (involving plays for Colorado, Nevada, New Mexico and Arizona)— as something of a fallback if efforts to win southern states such as Virginia and North Carolina stumble—in its calculations of how best to assemble 270 electoral votes in November.

For the Romney camp, any signs of strength into Southwest are a bonus—perhaps a big bonus.

Those are the presidential plays. There’s also the fight for control of Congress, and Democrats well recognize that getting a majority in the House requires them to hold marginal seats like the one in Arizona that Giffords won in 2006.

With the popular incumbent leaving, as she continues a recovery from a January 2011 shooting, Arizona Democrats have nominated her longtime aide Ron Barber

If the Republicans win it—as they desperately hope to do—that will be a boost for their hopes of securing a “trifecta” win in November, taking the presidency and the US Senate and keeping the US House.

When I was in Arizona recently, I saw Barber in action. He’s an old-school Arizona Democrat, with roots in the district and a style that suggests he would hit the ground running in Congress. Barber’s gotten some key newspaper endorsements and he has carefully distanced himself from Obama on some issues, while at the same time trying to pump up Democratic turnout. Barber says he’s running for “the people’s seat,” but his supporters all refer to it as “Gabby’s seat.”

Giffords campaigned Saturday for Barber (who was wounded on the same day she that she was shot and six others died). At a big rally in Tucson’s historic Rialto Theater, Giffords’ husband, Mark Kelly, said Tuesday’s contest was “more than an ordinary election” that could provide “closure for Gabby’s career in Congress.”

The Republican candidate for the Arizona seat, Jesse Kelly, ran against Giffords in 2010, and lost by barely 4,000 votes on a 48–47 finish. A 40-year-old Marine with close ties to the Tea Party and Sarah Palin, Kelly is running a very strong race.

And he’s got full support from the national party.

The National Republican Congressional Committee and its allies are “all in” with a slashing attack campaign that targets Barber, suggesting he would be a rubber-stamp for President Obama.

While the Democratic candidate in the race may actually raise more money than the Republican in official campaign accounts, the Republican is benefitting from an intense final spending push by Rove’s American Crossroads complex, Dick Armey’s Freedomworks and the right-wing American Action Network, along with full array of Republican Congressional committees and PACs.

Their message: if Kelly wins, they’re better positioned to keep not just the US House but the White House. “On Tuesday night, after we get victory, after we get there, this will be all over every news outlet out there in the whole country,” says Kelly. “Alaska will be watching. New York. They will all be watching what you did.”

By the same token, if Democrat Barber wins, the Democratic Southwestern strategy—for Congress and the presidency—will remain a live option.