President Barack Obama’s stirring words in Monday’s inaugural address offered his most soaring pledge in years to make a major assault on climate change — but that leaves the crucial question: “How?”

Prospects seem bleak for getting a major climate bill through Congress: If anything, the atmosphere on Capitol Hill has grown even more toxic since Obama’s proposal for a cap-and-trade system to throttle carbon emissions died without a whimper before the 2010 midterm elections. And unless the U.S. reins in its own carbon and persuades nations like China to go along, it’s going to be difficult to bring pollution levels down as sharply as scientists say is necessary to avoid calamity.

But climate activists say Obama has tools he can wield to bypass the gridlock on the Hill — including going ahead with tough EPA regulations on coal-burning power plants, offering more incentives for green energy and, contrary to the expectations of many, killing the Keystone XL oil pipeline from Canada.

Those types of actions would draw howls from congressional Republicans and cause heartburn for a number of Democratic lawmakers, some of whom face tough races in 2014. But greens said they drew hope from Obama’s words Monday, as well as from an unexpectedly rousing shout-out that Vice President Joe Biden gave them during a surprise appearance at an inaugural gathering Sunday night.

Some environmental advocates, including a couple former Obama aides, have also called for a reorganization within the White House to push climate and energy issues closer to the top of the agenda. One such approach — backed by former Obama transition team co-chair John Podesta and a coalition of activists and former senators — would create a White House energy council similar to those that oversee economic and national security policy.

Regardless of what management structure the administration uses, “I think the second term calls for somewhat of a different strategy,” Podesta said, adding that he sees leadership “as coming from the White House as opposed to just kind of letting each agency kind of figure out what to do.”

He said the administration could also reach out to businesses to create private-public partnerships to address climate and clean energy and pursue financing options for green energy at the Treasury Department, where “I think he could be much more aggressive.” That would dovetail with an existing green-fuels initiative at the Pentagon that has drawn harsh attacks from GOP lawmakers.

The environmentalists, deflated by Obama’s first term letdowns, are taking Monday’s pledges as a signal that his administration will no longer shy away from taking executive action that bypasses gridlock on Capitol Hill.

“We will respond to the threat of climate change, knowing that the failure to do so would betray our children and future generations,” Obama said — the kind of rhetoric that would be difficult for any president to walk back later.

After the cap-and-trade bill died, Obama himself said the emissions trading program was but “one way of skinning the cat.” The administration then began a series of steps to combat climate change from the Oval Office, although without the kind of high-profile rhetorical attention he gave to issues like his health care plan and the 2011 debt limit fight.

Then, in 2012, the White House grew altogether quiet on climate change. EPA officials suddenly began denying that they were working on greenhouse gas limits for existing power plants, which green activists consider imperative for any serious effort to rein in carbon.

Such rules could shift power generation in a way that significantly limits domestic demand for coal, which EPA critics warn would wipe out jobs and result in skyrocketing energy costs. That would no doubt inspire a pushback in Congress, especially from House Republicans who have repeatedly tried unsuccessfully to use interim budget deals or congressional resolutions to clip EPA’s regulatory powers.

Greens are hoping the president will put all his cards on the table.

Some of those cards come in the shape of court-ordered mandates, including from the Supreme Court, that have allowed the Obama administration to claim a legal imperative for climate change regulations.

Most crucially, the EPA seized on a 2007 Supreme Court ruling and declared that climate change poses a danger to human health and welfare. This in turn kicked off the legal domino effect in which EPA set first-time greenhouse gas standards for cars, and then proposed limits for new power plants.

The federal appeals court that typically handles EPA regulations has enthusiastically upheld the administration’s approach.

New steps from the administration are likely to come quickly in the second term. EPA is due to finish its rule for greenhouse gases from new power plants, which would allow it to segue to existing power plants — the largest source of climate-changing greenhouse gas emissions in the United States.

All that could come around the same time as the State Department is due to recommend that Obama approve or deny the Keystone pipeline.

One oil industry lobbyist recently stated that he is increasingly convinced Obama will reject the pipeline because approving it would rattle the president’s environmental supporters too much.

On the other hand, Obama hasn’t publicly drawn the same link as environmentalists have between the pipeline and climate change — greens say approving the pipeline will provoke a surge in oil production from the Canadian oil sands, causing massive new carbon emissions.

And some observers still think Obama has a way to finesse that decision.

Paul Bledsoe, a former Clinton White House climate aide, said Monday that the White House should seize on the common timing of the EPA regulations and the Keystone decision to establish a more comprehensive climate policy.

“If he approves Keystone, for example, he should announce at about the same time his broader climate change agenda — both domestic and international — to put that decision in policy perspective,” said Bledsoe, who’s now an independent consultant. “This is the kind of political salesmanship that real climate leadership will demand.”

On the other hand, anti-Keystone activists have said they’d see it as a betrayal for Obama to approve the project.

Still, environmentalists also want to see a broad plan from the administration.

“We are counting on President Obama to set tough limits on carbon pollution from power plants, continue investing in the development of clean, renewable energy sources, including wind and solar power, and to implement dramatic energy efficiency improvements that will cut dangerous pollution and protect our environment and our families,” Environment America Executive Director Margie Alt said Monday.

The Union of Concerned Scientists’ director of strategy and policy, Alden Meyer, said Obama and his team will need “a sustained campaign” to “overcome the opposition of entrenched interests to the rapid transition away from fossil fuels that’s needed to stabilize the climate.”