Sen. Hillary Rodham Clinton (D-N.Y.) may face a major character test — does she keep faith with her constituents in New York or go for the presidency in 2004?

Or, to put it tendentiously, is she a “Rodham” — a straight-forward product of the Midwest — or a “Clinton,” someone with an expedient interpretation of fidelity to promises of all kinds.

Sen. Clinton has pledged again and again and again to New York state voters that she will complete her first Senate term, which ends in 2007. She said at the New York State Fair last month that she “absolutely” will not run for national office in 2004.

And yet, her husband keeps dropping hints that she might run — the latest being that he was sure the voters of New York would understand if she changed her mind the way Arkansas voters did when he broke his pledge to stay their governor to run for president in 1992.

Sen. Clinton has to be sorely tempted to break her promise, given the decline in President Bush’s poll ratings and the attendant possibility that one of the 10 Democrats now running for his job might beat Bush.

This would probably block Sen. Clinton’s shot at the White House until 2012.

While Bush looked unbeatable, there was no reason why she couldn’t follow her original game plan — become a respected Senate heavyweight, campaign and fundraise diligently for Democrats in 2004 (including the sacrificial presidential nominee), get triumphantly re-elected in 2006, take the 2008 nomination almost for the asking and run against some relatively weak Republican for the open White House.

All this looked right on track until recently. But suddenly, Bush looks beatable and every poll around shows that Sen. Clinton is the overwhelming Democratic favorite.

The latest Quinnipiac survey showed that Sen. Clinton was favored by 45 percent of Democrats while all other contenders straggled in single digits behind her.

That poll also showed Clinton losing to Bush 52 percent to 42 percent and doing little better than the leading announced candidates. However, the ABC/Washington Post poll showed that Bush leads an unnamed Democratic opponent by just 5 points, 49-44.

Granted, it takes a Machiavellian interpretation to square Sen. Clinton’s running with her husband’s near-anointment of retired Gen. Wesley Clark, the latest entrant into the Democratic race.

The New York Times reported that Bill Clinton declared at a fundraiser for his wife in New York on Sept. 7 that there were “two stars” in the Democratic Party — his wife and Clark.

By implication, the nine other candidates aren’t “stars.” Various Clinton associates say the former president actually said that the eventual nominee would become a “star” when nominated and better known, but even that shows a bias toward Clark, who’s actually barely known to anybody outside the Pentagon.

And then, of course, there’s the fact that Clark is surrounded by former Clinton aides — former White House spokesman Mark Fabiani; Clinton’s longtime “body man,” Bruce Lindsey; and 1992 campaign aides Eli Segal and Mickey Kantor.

Somebody in the Clark campaign even leaked it to Fox News’ Carl Cameron that Sen. Clinton was going to be Clark’s campaign co-chairwoman, which her office immediately denied. But the story underscored the close Clinton-Clark connection.

So, why would the Clinton gang build up Clark if Sen. Clinton was going to run? Well, the Machiavellian interpretation is: to diminish all the other candidates and, especially, stop Howard Dean’s near-runaway progress toward the nomination.

As many commentators have noted, Clark is an anti-Iraq war “outsider” like Dean, yet vastly more credible on national security issues. He is a war hero who cuts into the appeal of war-hero Sen. John Kerry (Mass.). He’s from Arkansas, diluting the Southern base of Sen. John Edwards (N.C.). And he can bite into the moderate/hawk following of Sen. Joe Lieberman (Conn.).

The Clinton/Machiavelli plan would break down if Clark caught fire and seized the nomination. But chances are that, as a political novice starting late, he’ll just complicate Dean and Kerry’s bids for the nomination.

That would produce a situation where none of the 10 candidates looks particularly strong, but the White House looks within reach of somebody who is strong. And who would Democrats love to turn to? Why, it could be organized in no time.

Now, I have to admit that close Clinton advisers say this is all nonsense. Asked the percentage chance that Sen. Clinton would run next year, one of them said “2 percent — it would happen only if a hurricane killed the two top candidates. She is not reconsidering her promise.”

And yet, to this and other Democrats, the White House definitely looks within reach. Bush’s approval rating is down to 52 percent in some polls.

Would Sen. Clinton accept the vice presidential nomination? That, too, would essentially violate her pledge not to run in 2004. And it would enhance only a little her already-spectacular chances of winning the nomination in 2008. If she helped the ticket win, she’d have to play second fiddle for eight years.

So, the final Machiavellian question becomes: How do the Clintons campaign for the 2004 nominee and still make certain he loses to Bush? That one, I can’t figure out.