WASHINGTON — Lessons from the off-year elections: The president’s influence is limited, independents rule, incumbents beware, issues trump ideology and, once more, “It’s the economy, stupid.”

Also: Republicans can win — even if they lack a leader and their base is cracked. And this certainly isn’t the Democratic-friendly political environment of 2006 and 2008 when the party captured control of Congress and the White House.

The first Election Day of Barack Obama’s presidency was a big night for Republicans, who recaptured governorships in the swing state of Virginia and the Democratic stronghold of New Jersey. Democrats won two races for vacant congressional seats, including one in upstate New York that had been long held by Republicans and that exposed a GOP divide.

So, what did we learn about politics, people and their priorities from the handful of races on Tuesday? And how will those lessons shape the maneuvering of Republicans and Democrats ahead of 2010 midterms, when Obama’s prestige will be put to the test across the country?

The results don’t seem to bode well for Obama and his party heading into a high-stakes year as they look to advance an expensive domestic agenda while protecting the Democrats’ grip on House, Senate and gubernatorial seats nationwide. They’ll try to win over people in a country clouded by a job-killing recession, divided over war and, as Tuesday’s results showed, fed up with the powers that be — no matter the political party.

Among the lessons learned:

Obama’s political power is limited

The broad coalition — minorities, young people, first-time voters, Republican crossovers and independents — that fueled Obama’s victory was a 2008 phenomenon; it can’t be counted on if the man himself is not on the ballot. Even though Obama personally implored his supporters to turn out in droves, voters rejected incumbent Democratic Gov. Jon Corzine in New Jersey and Democratic candidate R. Creigh Deeds in Virginia.

That could be a problem for Democratic lawmakers in swing states and conservative-to-moderate districts next fall because Obama won’t be on the ballot to drive up turnout. Candidates carried into office in the Obama wave will be vulnerable in 2010 — with no lifeguard to help. And that could influence how those lawmakers vote in Congress in the meantime — perhaps threatening the president’s priorities.

With Obama unable to guarantee their political survival, what’s the incentive for them to back his legislative agenda?

Independents

are kingmakers

Voters who don’t claim a political party again proved their value by propelling Republicans to victory in Virginia and New Jersey one year after carrying Obama to the White House.

Independents are, well, truly independent — and, thus, are extraordinarily fickle.

Last year, hope and change tilted them toward Democrats. This year, anger and frustration tilted them to Republicans. They broke 2-1 for GOP victors Chris Christie in New Jersey and Bob McDonnell in Virginia.

Issues, from jobs to taxes to government spending, drive this center of the electorate, so candidates who talk about what independents care most about will win the middle and, thus, elections.

Democrats must figure out a way to bring independents back into their fold — or risk huge losses next fall.

Still, Republicans must be mindful of the volatile nature of public attitudes, for independents who have moved toward the GOP since last fall could just as easily move back to the Democrats by next November.