President Obama was sworn in for his second term at a White House ceremony on Sunday. Chief Justice John Roberts admistered the oath of office. (The Washington Post)

As President Obama begins his second term, he faces a difficult, if familiar, conundrum: Much of the ambitious agenda he has laid out for the next four years requires action from a sometimes hostile Congress.

Rarely have a president and a Congress been as intractably at odds as Obama has been with the Republicans who control the House and hold the power to block his agenda with the filibuster in the Senate.

Rather than a moment of renewal, Monday’s public presidential swearing-in is likely to serve as only a brief cease-fire in the fights that have consumed the White House and Capitol Hill since Republicans swept the House two years ago.

At the core of Obama’s fractious relationship with Congress has been a running battle with Republicans over taxes and spending, and the pomp and circumstance of the inauguration will probably do little to ease the tensions that fuel that struggle.

The last dispute in that fight — the year-end clash over how to avoid the “fiscal cliff” — will bleed seamlessly into the next fight over whether to raise the nation’s $16.4 trillion borrowing limit.

The oaths: From Washington to Obama

A new proposal unveiled Friday by House Republican leaders to extend the nation’s borrowing authority for the next three months could offer both sides a bit of breathing room. But their goal was not to disengage from the spending battle but to boost GOP leverage as discussions roll into the spring.

What happens in the next 90 days on that front could prove critical to the fate of the rest of Obama’s legislative agenda, including attempts to reform the nation’s immigration system and institute sweeping new gun-control laws.

Second-term presidents usually enjoy a post-election glow of up to eight months, said James A. Thurber, a professor who studies Congress and the presidency at American University.

“He’ll have barely a month,” Thurber said of Obama, arguing that the debate over the fiscal cliff, in which Republicans unhappily agreed to allow taxes to rise on those making more than $450,000 a year, has left Washington with a toxic hangover.

“I don’t like the cliff analogy. I think it’s been more of an avalanche,” he said. “We’ve had an avalanche of work that really undermines his political capital and undermines the capacity to come together.”

The fights over spending could swamp Obama’s call last week for new background checks for gun buyers, a reinstituted ban on assault weapons and a restriction on high-capacity magazines.

House Republicans, deeply opposed to new gun-control laws, said they spent virtually no time on the topic at a closed-door retreat in Williamsburg last week where they sketched out legislative plans for the next year.

Broad changes to the nation’s immigration laws would seem to have brighter prospects in Congress. At the retreat, Republicans were told by several speakers that the party must join with Democrats to support immigration reform or risk becoming a permanent minority as the number of Latino voters grows.

But there exists significant opposition among some Republicans to changes that could be seen as amnesty for people who entered the country illegally. Changes will require a level of across-the-aisle cooperation between the White House and individually supportive Republicans rare over the past two years.

But first, Congress will address a series of complex fiscal decisions.

In addition to dealing with the debt ceiling by early March, Congress must also decide whether to allow deep and arbitrary cuts to the military and domestic programs to take effect. By the end of that month, it must decide how to fund the government for the next year when the current spending plan expires.

Both are moments Republicans hope to use to force Democrats to concede major cuts in entitlement programs.

If Obama could reach a broad deal with Republicans in the next three months that settled central disputes over entitlement spending and the tax code and gave the government borrowing authority to last through much of Obama’s second term, he could find new energy and oxygen for bipartisan action on other issues.

Neither side has expressed particular optimism over that outcome.

Alternatively, failure to reach deals — particularly on the debt ceiling — would result in uncertain political and economic chaos, as the government experienced its first-ever technical default.

Obama has warned that if Congress does not act by late February or early March, the government will be unable to issue Social Security checks or veterans benefits. Portions of the government would be shuttered.

Federal agencies would also close if the parties do not agree on a new basic spending plan for the next fiscal year by March 27.

Many conservatives think a government shutdown could provide a healthy jolt to the system that would force Obama to take Republican concerns about spending increases more seriously.

Liberals think the public would hold Republicans responsible for the economic upheaval. The popular backlash could result in a deep fissure in a Republican Congress already in disarray, potentially freeing a small group of moderates to break party ranks and work with Democrats on other issues.

“This is a high-risk, make-or-break situation that you only see every three or four decades,” said Scott Lilly, a senior fellow at the Center for American Progress and a former Democratic congressional staffer. “I think the big question in my mind is, ‘What is the House Republican conference going to look like a year from now?’ I think anybody who says they know the answer to that is overstating their competence.”

The outcome most in keeping with the pattern of the past two years would be short-term compromises — much like the GOP’s three-month debt-ceiling increase that will face a House vote Wednesday. Such moves would spare the country the economic consequences of failing to act entirely but require revisiting the central dispute every few months.

“There’s a good chance this continues into the summer and beyond,” said Steve Bell, a former Republican staffer who works for the Bipartisan Policy Center. “If that’s true, it’s going to be very difficult to concentrate on immigration or guns or anything, when you have all of the scar tissue being created by this interminable fight.”