Rand Paul seems to be crossing over to the mainstream — or maybe it’s the other way around.

When Kentucky’s junior senator arrived in Washington just over two years ago, he appeared destined to inhabit the role of perpetual outlier. But now, he’s in the mix on just about everything that is happening, and is talked about as a credible Republican presidential contender in 2016.

Paul is aggressively trying to forge at least a cordial relationship with GOP establishment interests that have been suspicious of him — sometimes even outright hostile — in the past.

“He is a work in progress,” said one well-known Republican who recently met with Paul and spoke on the condition of anonymity, sensitive to the fact that public knowledge of their cordiality wouldn’t benefit either of them.

Part of his new relevance comes from the sudden prominence of a set of issues on which Paul has been a somewhat lonely voice in the Republican Party.

There is fresh attention to privacy, amid revelations about the government’s aggressive surveillance programs; renewed mistrust of the Internal Revenue Service, in the wake of its admissions of improperly targeting conservative groups for scrutiny; and heightened anxiety about foreign entanglement, as the prospect of deeper U.S. military involvement in Syria looms.

Meanwhile, Paul is involving himself more deeply in other questions where he has not been a leading player in the past.

On immigration, for instance, he has introduced a series of amendments to increase congressional oversight of border security and narrowly define the conditions under which those who are in this country illegally can get in line to become citizens.

“I am the conduit between conservatives in the House who don’t want [a broad bill] and more moderate people in the Senate who do want these things,” Paul said recently on “Fox News Sunday.” “I’m really trying to make immigration work. But they’re going to have to come to me, and they’re going have to work with me to make the bill stronger if they want me to vote for it.”

What most explains the new seriousness with which Paul is being regarded, however, is the quest for identity inside the battered Republican Party.

In an era of government expansion and mounting debt, the GOP is undergoing something of an evolution in its attitude toward the libertarian philosophy of Paul and his father, former congressman and presidential contender Ron Paul (R-Tex.).

“Most people like me — Republican, conservative — have a libertarian streak in them,” said Vin Weber, a lobbyist, ex-congressman and pillar of the party establishment in Washington. “Whereas 20 or 30 years ago, Republicans would say the real world prevents them from acting on their libertarian instincts, today the real world is heightening their libertarian instincts.”

Others say that the younger Paul, 50, has helped bring about more acceptance of libertarianism by offering a softer-edged ideology than his father’s.

“I would define Ron Paul as a hyper-libertarian,” said David Lane, a Christian conservative activist who organized a seven-day trip to Israel for Paul and a group of evangelical pastors in January. “I think [Rand Paul] is closer to where I am philosophically than he is to where his dad is.”

Still, many aspects of libertarianism remain a hard sell to key Republican constituencies, particularly to social conservatives who see its mind-your-own-business attitude as an abandonment of moral values, and to internationalists who believe its tendencies toward isolationism are dangerous and naive.

“He still is going to have to explain how America leads in the world. You can’t discount all the tools in the toolbox,” Weber said. “At some point, he has to articulate a philosophy of what it is that government should appropriately be doing.”

Paul’s office declined a request for an interview.

Bigger tent

The Kentucky opthalmologist-turned-senator represents a brand of inclusiveness at a time when the party is desperate to reach beyond its base. Along with his father, he also has an ability to excite young people that no one else in the party can match. In March, his 13-hour filibuster to protest the Obama administration’s drone warfare tactics electrified the blogosphere on both the left and right, with Twitter registering 450,000 tweets using the hashtag #standwithrand.

“If we want to win nationally again, we will have to reach out to a diverse nation and welcome African Americans, Asians, Latinos into our party. When the Republican Party looks like the rest of America, we will win again,” Paul said in a well-received speech on March 31 at the Ronald Reagan library in Simi Valley, Calif. “When we have people with tattoos and without tattoos, with ties and without ties, with suits and in blue jeans, then we win nationally.”

Paul’s outreach efforts have not been unvarnished successes. He was lampooned last month, for instance, for giving an awkward presentation about the Republican Party’s role in the civil rights struggle before an audience of African American students at Howard University.

But what impressed many was the fact that a Republican went to Howard at all.

“His audience was the outside world, and [his message was] the fact that he showed up. The easy thing would be not to go,” said former congressman J.C. Watts (Okla.), one of the few prominent black Republican lawmakers.

Watts said he recently met with Paul to discuss working together on their mutual interest in changing mandatory sentencing laws that both believe are disproportionately harsh on African Americans.

“Rand Paul is willing to admit that’s a real issue. That’s something conservatives often don’t want to do is admit the reality of the problem,” Watts said. “You don’t have to abandon your conservative values to admit there’s a problem.”

Watts acknowledged that his perception of Paul has changed. He compared his reaction to the old tag­line of late-night television host Arsenio Hall: “Things that make you go, ‘Hmm.’ ”

When Paul won his party’s nomination in 2010 — on the strength of tea party support, and over the establishment pick backed by Senate Minority Leader Mitch McConnell (R-Ky.) — the Republican Jewish Coalition, which includes many of the party’s biggest fundraisers, was so horrified that it took the unusual step of opposing a Republican.

At the time, RJC Executive Director Matthew Brooks said Paul was “outside the comfort level of a lot of people in the Jewish community, and in many ways, outside of where the Republican Party is on many issues.”

But a thaw may be in the offing, after a meeting last week with the organization’s board of directors.

“There were some pleasant surprises,” Brooks said. “While there may be areas of disagreement, he is very, very different — and certainly different with regard to his father.”

Although Paul persists in wanting to end foreign aid, for example, he described that as an eventual goal, and talked of “putting Israel in a different category” from that of hostile countries, Brooks said.

Lined up for 2016?

In recent months, Paul has schmoozed major Republican contributors at events that included an April conference in California sponsored by mega-donor brothers Charles and David Koch and a gathering of 2012 GOP presidential nominee Mitt Romney’s financial backers in Utah this month.

He also has been making appearances in early presidential primary states — and in nontraditional venues for Republicans, such as libertarian-minded Silicon Valley.

At this point, the recent political phenom Paul most resembles may be one from the other party — former Vermont governor Howard Dean, also a doctor, whose briefly front-running 2004 Democratic presidential campaign excited passions and threatened to upend the establishment, but ultimately crumbled to make way for a more conventional nominee.

For Paul, too, the question ultimately may be whether he has the discipline and the seasoning to go the distance.

But for now, he remains a figure of singular intrigue, no longer marginalized by his party — or dismissed by the opposition.

The current cover of the left-of-center New Republic magazine features a black-and-white image shot by the edgy portrait photographer Platon. “The Real Rand Paul (Can’t Be Trusted),” it warns. The fingers on his left hand are crossed.