1 of 34 Full Screen Autoplay Close Skip Ad × Election night 2014 View Photos Republicans cruise to Senate majority, expand their advantage in House Caption Republicans cruise to Senate majority, expand their advantage in House Senate Minority Leader Mitch McConnell speaks to his supporters, with wife Elaine Chao at his side, after being declared the winner in the Senate race in Kentucky. Melina Mara/The Washington Post Buy Photo Wait 1 second to continue.

Now that power has changed hands in the Senate, there are two scenarios for what is likely to get done in Washington over the next couple of years: not much, and nothing at all.

The new Republican majority was elected with virtually no agenda beyond stopping President Obama’s — something the GOP senators were already pretty successful at doing as the minority.

Their leader, Mitch McConnell (R-Ky.), preoccupied with his own reelection, has conspicuously avoided setting out any grand ambitions — such as putting entitlement programs on sound financial footing, or overhauling the immigration system, or rewriting the tax code.

“There are some obvious things. We’d be voting on the Keystone pipeline” as well as several modifications to the Affordable Care Act, McConnell said at a campaign stop Friday. “A number of things that, I think, there’s a majority in the Senate for.”

But “voting on” legislation is not the same thing as enacting it. Republicans will be short of the 60 votes needed to overcome filibusters by a Democratic minority that is expected to feel little incentive to compromise. The Republicans would have to have even more — 67 — to override a presidential veto.

Thus far, Obama has used the veto only twice during his presidency, on bills that had technical flaws, but aides say he is ready to assert that power as frequently as it takes to protect the things he cares about.

That is why the goal most often mentioned by this year’s Republican candidates — repealing Obama­care — remains out of reach.

“Practically speaking, with President Obama in the White House, that’s probably not going to happen,” McConnell said.

“But we’ll certainly be voting on it,” he added.

McConnell and Obama each offered a gesture of cooperation Tuesday.

As results began to show the early signs of a strong Republican night, the White House let it be known that Obama had invited the bipartisan congressional leadership for a meeting on Friday. And McConnell, in his victory speech, pointed to an “obligation to work together on issues where we can agree.”

“Just because we have a two-party system doesn’t mean we have to be in perpetual conflict,” he said.

Meanwhile, House Republicans, who were expected to expand their majority Tuesday, say they will recycle a raft of bills, most of them relatively narrow in scope, that they’ve passed before but never gotten through the Senate. Among other things, those measures would open up more oil and gas drilling, require government agencies to disclose more about their process of writing regulations, and encourage employers to hire more military veterans.

On the other end of Pennsylvania Avenue, White House Chief of Staff Denis McDonough has been holding regular meetings with Obama’s top aides in recent weeks to map out a strategy for the final two years of his presidency, factoring in the new alignment of power on Capitol Hill.

There is a sort of fatalism in their calculations. “We will be open to opportunities where we can work together but realistic about the larger political dynamics that have stymied progress so far,” said senior presidential adviser Dan Pfeiffer.

Barring an unlikely outbreak of bipartisanship, Obama plans to focus on things that remain largely within his control: foreign policy, the ongoing implementation of the health-care law, regulation of financial markets and other laws passed early in his presidency.

Obama also plans to use his executive authority, aides said.

One much-anticipated order would allow some yet-to-be-determined number of illegal immigrants to remain in this country, a move likely to inflame the issue just as both parties try to regroup before the 2016 elections and court crucial Hispanic voters.

Other executive orders could come on climate change, White House press secretary Josh Earnest said Tuesday, adding a less-than-subtle suggestion that Democrats see political upsides in drawing the GOP into a more robust debate on that front.

“There are still, you know, too many Republicans in Congress who even deny the basic scientific fact that climate change is occurring and something that policymakers should be concerned about,” Earnest said. “So the president will use his executive action to take some additional steps, but he is also going to continue to talk about this issue in a way that lays the groundwork for action by future presidents and future Congresses.”

The GOP gained control of the Senate Tuesday night, taking hold of the legislative agenda in that chamber. Here are three of the policies Republicans are likely to tackle as they take the reins in January 2015. (Julie Percha/The Washington Post)

Obama also has an eye on his legacy, and on softening the turf for presidents who follow him to act on issues that matter to him.

Even after an election in which largely unregulated outside groups spent an unprecedented $500 million on congressional races, the chance of passing campaign finance reform legislation “is rather remote,” Earnest said. “But the president is going to continue to talk about that issue, and he’s going to continue to try to push that issue.”

Before the new Congress is sworn in, there will be a closely watched lame-duck session in which Democratic and Republican lawmakers will be able to test their realigned relationship.

Senior aides in both parties say that, at a minimum, the Senate will have to agree on a bill to fund the government, to reauthorize operations in Syria, prevent a tax increase on the Internet and pass a defense policy bill.

Senate Majority Leader Harry M. Reid (D-Nev.) is also expected to use his final days in charge of the chamber to push through as many Obama nominees as he can — possibly including the president’s yet-to-be-announced pick to replace Attorney General Eric H. Holder Jr.

Then Republicans will get the reins.

There is a case to be made that the new majority will feel compelled to rack up some achievements, if for no other reason than to show that the Republican Party that was blamed for a 16-day federal shutdown last year knows how to govern.

The electoral map in 2016 will be a hostile one for the GOP — almost an exact inverse of this year’s — with 23 Republican-held seats on the ballot, many of them in states carried twice by Obama. Those facing reelection may feel intense pressure to move toward the center.

But it is just as easy to argue that partisan lines will be hardened. About half a dozen Senate Republicans are seriously considering running for president, which means they will be playing to the party’s conservative base. One of them, Ted Cruz of Texas, told The Washington Post last weekend: “I think we have seen election after election that when Republicans fail to draw a clear distinction with the Democrats, when we run to the mushy middle, we lose.”

Senate Democrats, meanwhile, are expected to hunker down. It will be in their political interest to resist giving the GOP any legislative victories to claim, and to keep the distinctions between the two parties as sharp as possible in the run-up to 2016.

The last two men who found themselves in McConnell’s situation say he will soon learn how much more difficult it is to be the leader of a fractious majority than the organizer of a block party.

“Minority leader is a lot easier. It’s much more defense, trying to stop things you don’t like,” said former senator Trent Lott (R-Miss.).

Former senator Thomas A. Daschle (D-S.D.) noted that as majority leader, “you must work with the minority leader, the speaker, the president and your caucus. The latter is sometimes hardest of all, because there are some who believe they can do the job better than you can. And almost immediately, there is the next election.”

McConnell is an institutionalist who got his start on Capitol Hill as an intern and Senate aide in the 1960s. His first goal, those around him say, is to restore a semblance of “regular order” to the Senate: hashing out bills in committee, getting appropriations bills passed on schedule, allowing more amendments on the floor, making sure the Senate passes a budget — something that has happened only once since 2009.

And there are a few pieces of legislation in which significant agreement already exists between the two parties. Some that might actually get to Obama’s desk and be signed into law: new spending on infrastructure, trade bills, changes in the corporate tax code. And, yes, the Keystone XL oil pipeline that has been a point of tension between the parties and within the Obama administration.

Those may sound like small things compared with the grand bargains that once seemed possible. But, said Lott, who knows? “Do some of those things, and show you can get things done, and it becomes contagious.”

Paul Kane and Ed O’Keefe contributed to this report.