WASHINGTON — Mitch McConnell has an unusual admonition for the new Republican majority as it takes over the Senate this week: Don’t be “scary.”

The incoming Senate majority leader has set a political goal for the next two years of overseeing a functioning, reasonable majority on Capitol Hill that scores some measured conservative wins, particularly against environmental regulations, but probably not big victories such as a full repeal of the health law. McConnell’s priority is to set the stage for a potential GOP presidential victory in 2016.

“I don’t want the American people to think that if they add a Republican president to a Republican Congress, that’s going to be a scary outcome. I want the American people to be comfortable with the fact that the Republican House and Senate is a responsible, right-of-center, governing majority,” the Kentucky Republican said in a broad interview just before Christmas in his Capitol office.

It’s a far cry from his defiant declaration in 2010 that his “single most important” goal was to make President Barack Obama a one-term president, an antagonizing oath that Democrats frequently invoke to embarrass the GOP leader — Obama won re-election comfortably in 2012, and McConnell’s party lost seats.

Now in charge at both ends of the Capitol, Republicans aim to avoid the worst excesses of the past four years and make sure the public isn’t fearful of the GOP’s course.

“There would be nothing frightening about adding a Republican president to that governing majority,” McConnell said, explaining how he wants voters to view the party on the eve of the 2016 election. “I think that’s the single best thing we can do, is to not mess up the playing field, if you will, for whoever the nominee ultimately is.”

But McConnell is not planning to avoid conflict altogether. He wants to use the annual spending bills to compel Obama to accept conservative policy riders that will divide Democrats, similar to the December spending bill’s inclusion of a provision benefiting Wall Street firms involved in risky derivative trades. That rider brought a liberal outcry but did not end up torpedoing the bill, which had Obama’s support.

McConnell has been coaching his members to understand that, in the initial rounds, they will have to almost unanimously support the budget outline and the spending bills, because few Democrats will support their policy riders.

With 54 Republicans in his caucus, McConnell knows that he’s a long way from getting 67 votes to override Obama’s veto and that it won’t even be easy getting six Democrats to regularly support legislation so he can overcome likely filibusters led by the incoming minority leader, Sen. Harry Reid, D-Nev. Still, on some issues, such as energy and taxes on the health industry, McConnell thinks there’s enough bipartisan support to get bills onto Obama’s desk.

“They’d like to be relevant. They’d like to be part of the process,” he said of discussions with some rank-and-file Democrats. “Assuming we will have on most issues a largely unified conference — I don’t expect that on everything — it wouldn’t take a whole lot of Democrats to actually pass legislation in the Senate.”

But McConnell said those who are “craving some grand deal as a way to measure the next two years” should lower their expectations. He’s very skeptical of such bargains with Democrats on tough issues such as immigration and entitlement reform. Instead, he believes three issues have potential common ground: international trade deals, an overhaul of the tax code and new revenue streams for infrastructure projects.

“Could the country use a lot more? You bet. But there’s no way you can overcome a reluctant president on something really large,” McConnell said. The best he can do on some of those bigger issues is force Obama to break out his veto pen so there is a clear set of Democratic policy stances Republicans can campaign against in 2016.

Democrats are dubious of McConnell’s pledge to avert edge-of-the-cliff moments. They believe he will run into the same problems that have bedeviled House Speaker John Boehner, R-Ohio, during the past four years — including the inability to corral rabble-rousers such as Sen. Ted Cruz, R-Texas, to support an agenda that conservative critics will probably view as not bold enough in challenging Obama. Appeasing those far-right conservatives will lead to an agenda that Democrats hope to exploit in 2016.

“What Senator McConnell wants people to think and what they will think when they see the results for themselves are two very different things,” said Reid’s spokesman, Adam Jentleson. “Senator McConnell heads a caucus that is obsessed with rigging the game against working people in favor of wealthy special interests. That’s a scary fact indeed, and he won’t be able to hide it.”

GEORGE MITCHELL WANNABE?

While McConnell’s office is adorned with a portrait of Kentucky’s only other Senate majority leader — Alben Barkley, whose tenure was often marked by clashes with his own party’s president, Franklin Roosevelt — his model more resembles that of George Mitchell, the Democratic majority leader from 1989 through 1994.

Without ever shutting down the government, Mitchell stared down a president of the opposite party, George H.W. Bush, and won several liberal victories in a 1990 budget showdown. Mitchell also delivered a slew of legislation to Bush’s desk that drew a veto, helping frame the debate for the 1992 election on domestic policy.

McConnell has recently studied other two-term presidents on how often they vetoed legislation in their last two years in office. Obama has issued only two minor vetoes over technical matters, largely because the previously Democratic-run Senate prevented anything from reaching his desk that he opposed.

McConnell suggested that a veto strategy would help clarify issues for voters. “I think his bureaucracy across the board has done a lot of damage to the country. . . . I’d at least like for him to have to personally take responsibility for it, even if he in the end decides to veto the bill over some restriction on EPA regulations.”

USING THE R WORD

McConnell is keenly aware of the challenges of reining in some of the impulses that his fellow Republican lawmakers have developed over eight straight years in the minority.

The first test will come on an energy debate, which could begin by the end of this week. McConnell is trying to keep his side from offering amendments not related to energy issues. In recent years, when some rank-and-file Republicans wanted to stop the Senate in its tracks, they would threaten amendments related to how Congress gets its health care.

“I’ve asked my members to restrain themselves,” he said.

Restraint has been hard to come by in this political era, particularly because a small army of conservative groups has made it a mission to push Republicans to the most strident stands, even if it means shutting down the government or risking default on the national debt.

McConnell faced some of those groups firsthand when they supported his 2014 primary challenger, and he faced a grinding general election against a Democrat who was well financed.

It cost nearly $30 million from his campaign war chest and tens of millions of dollars more from outside groups. Winning both races handily, McConnell is delivering a message to Republicans on how to behave heading into 2016.

“Don’t try to reinvent yourself. Be yourself, number one. And don’t be afraid of a primary. We will win all the primaries. We did it in ’14. We will do it in ’16,” McConnell said.

Shortly after Election Day this fall, McConnell sat down with Obama for a rare one-on-one meeting in the Oval Office, a huddle that both sides kept largely secret. In the pre-Christmas interview, McConnell acknowledged that the meeting’s purpose was only to discuss areas where the president and Republicans might find bipartisan agreement — because their disagreements on other issues were too intractable.

That meeting, he said, focused on trade deals, a tax code overhaul and infrastructure funding. “Can we get there on tax reform, trade, infrastructure?” he said.

He eschewed the idea of holding the debt ceiling hostage to gain spending cut concessions from Obama, a tool Republicans had to use before because they were in the minority.

“We are in the majority. We can pass a budget. We can determine how much we’re going to spend,” he said.

Avoiding those moments could make for a less “scary” Congress, giving the Republicans a better chance in 2016 to hit the trifecta and gain the White House. His own horse is already chosen, Sen. Rand Paul, R-Ky., but don’t expect McConnell to be out on the campaign trail or doing any other favors for his home-state colleague.

“I’m going to be supporting Rand Paul. But he knows that beyond that, I won’t be involved in presidential politics. I’ve got a big job here,” he said.