President Barack Obama says his Republican challenger has the “wrong vision” for the country. So what’s his?

Some of his agenda for a second term is a continuation of the first. He’d raise taxes on annual family incomes above $250,000. He’d continue to spend on education and green energy. He’d implement the health care law and financial regulations already enacted. And he’d continue to withdraw U.S. combat troops from Afghanistan with a goal of getting them all out by the end of 2014.

Much of his plan is an open question, though, rendered all the more mysterious when he was caught on an open microphone telling Russian President Dmitry Medvedev earlier this year that he’d have “more flexibility” after the November election. To do what isn’t yet clear. Though he’s offered broad themes on the campaign trail, Obama has yet to flesh out the details.

What should Mr. Obama push for? The richest American earners must pay more taxes on personal incomes, but the president should also propose comprehensive tax reforms to level the business playing field and encourage growth. A modest carbon tax should also be part of the mix—and I would strongly favor using the revenues to pay equal dividends directly to each American. Dividends would do more for low- and moderate-income families, buffering them against higher energy costs and boosting consumer demand. They also would give all citizens a visible and easily understood stake in the transition to a greener economy…

Perhaps the GOP will remain grumpy about the Affordable Care Act through 2014 and refuse to cooperate on routine legislative fixes. But a second Obama administration can move full speed ahead with the states. With repeal no longer possible, governors of both parties will have strong incentives to accept most Medicaid expansions and get the new health-insurance exchanges right. Mr. Obama should continue to welcome state-level experimentation, so that the best solutions can be found and spread across the land.

Above all, we need to slow, stop and reverse climate change. A generation ago, as we faced another man-made global threat, the United States provided the leadership that produced an international agreement to ban chlorofluorocarbons from consumer products. Those chemicals had been destroying Earth’s life-protecting ozone layer.

The coming 25th anniversary of that Montreal Protocol serves as a timely reminder as we confront this generation’s planetary crisis: The world can come together. We can conquer climate change.

Doing so starts with presidential leadership, and the Obama administration has made a good start—most notably through carbon-reducing performance standards like the auto fuel-efficiency standards it issued last week. Fundamentally, though, Americans will need to finally put a price on carbon pollution.

The president should approach the Republican leadership with an outstretched hand on a broad front of issues and be prepared to consider steps he has resisted. By doing so, he’ll seize the political high ground. And if the Republicans join him, his second administration would have the best chance to leave the country in better shape than he found it in 2009.

Here’s some of what this might mean:

Reaching a long-term fiscal agreement somewhere in the zone demarcated by the Simpson-Bowles and Domenici-Rivlin commissions.

Stabilizing the long-term finances of Social Security within the framework of the current program, which could be achieved through modest and well-understood changes in both revenues and benefits. For example, earnings subject to the Social Security payroll tax could be gradually raised to 90% from 85%, while benefits for upper-income beneficiaries could be indexed to inflation rather than wages.

If Barack Obama wins re-election, Republicans will accept the fruitlessness of strategic obstruction. Unencumbered by the imperative to defeat Obama, who will be a lame duck president anyhow, they will begin to work with him on matters of urgent importance to the country.

That’s the White House’s operating theory, anyhow. In their words, the GOP’s fever will break. Or, as Obama himself recently put it, the “blister” will pop, and a new birth of good will will ooze forth into our politics.

There’s just one problem with the theory. Republicans and conservative thought leaders both openly say Democrats are kidding themselves. Even if Obama wins, the GOP is prepared to stymie him all over again — unless he more or less adopts a Republican governing agenda. Some have even used the promise of ongoing obstruction as an argument for a Romney president: Better to let us run the whole show than to keep government divided, because we won’t work with Obama if that happens.

It’s a brazen admission, and one the White House doesn’t really have an answer for.

Senate Minority Leader Mitch McConnell (R-Ky.) said Thursday that if President Barack Obama is reelected, there would be potential under a divided government to make real progress on tax reform and entitlements.

With one caveat.

“I think it depends on whether Obama has an epiphany,” McConnell said in an interview…

“People ask me all the time to kind of psychoanalyze the guy, because I know him pretty well. I have no idea what he really is like,” McConnell said. “I can only assess what he has done. And what he has done so far is neither Reagan-like or Clintonian. And I can’t predict what he would be like in a second term. But I know this: he will not be able to do anything like what he did in the first two years.”

If Obama wins, he will almost certainly win with a smaller majority of the vote than he got in 2008, in defiance of the usual trend: Incumbents who win re-election usually do better the second time around. Republicans will almost certainly add to their ranks in the Senate, and may take a majority. No way would they see this set of election results as a “decisive” statement of support for Obama’s views…

The Republicans aren’t going to change. Judging from the interview, neither will the president. He said that after the election he would tell Republicans “you no longer need to be focused on trying to beat me; what you need to be focused on and what you should have been focused on from the start is how do we advance the American economy.” He would reiterate that he has always been open to compromise. And he would “look at how we can work around Congress,” if needed…

If the public renders a split verdict — returning Obama to the presidency and giving Republicans more power in Congress — both parties will insist that it’s the other that needs to “listen to the American people.” The choice before those people is looking more and more like one between Romney and a unified Republican government, or Obama and four more years that look a lot like the last two.

Personally, I wish Obama would use this convention to embrace Bowles-Simpson. That would lay the foundation for decades of prosperity. It would galvanize a new center-left majority.

But, mostly, I wish he’d be for something. I wish he’d rise above the petty tactical considerations that have shrunk him over the past two years. I wish he’d finally define what he stands for. A liberal populist? A Clintonian moderate? At some point, you have to choose.

Four years ago, Obama said we could no longer postpone tackling the big problems. But now he seems driven by a fear of defeat. His proposals seem bite-size. If Obama can’t tell us the big policy thing he wants to do, he doesn’t deserve a second term.

Nevertheless, the Obama team remains cautiously confident that they are on track to win reelection for the President. As David Plouffe put it in an interview with me, while Obama advisers fully expect the race to be extremely close until the end, as long as he maintains a small but persistent lead in the battleground states, “we’re right on the cusp of victory.”…

The Romney camp seems to be hoping for a big, late break of undecided voters his way. But Dems remain convinced they understand who these voters are and what motivates them better than the Romney team does — and don’t see a way that these voters break to Romney in large enough numbers to overcome a two or three point deficit in the key battlegrounds.

“The question is, Is Romney going to get enough of the undecided vote to overcome a two or three point deficit in the battle ground states?” Plouffe told me. “Most assuredly not.”