It's the candidacy that must not be named.

Not by some Capitol Hill Republicans, at least, who have largely resigned themselves to the reality of reality TV star Donald Trump as their presidential nominee, but can't quite seem to utter his heavily branded name even as they declare their support for a man who has all but sewn up the nomination and paid a visit to their domain on Thursday.

Does Alabama Sen. Richard Shelby endorse Donald Trump for president?

"I've endorsed the nominee. He's the presumptive nominee, and I'm going to vote for him and support him," Shelby answers, without mentioning Trump by name.

What about Thom Tillis, a freshman senator from North Carolina – would he describe himself as enthusiastically endorsing Trump?

"I enthusiastically support the nominee," parries Tillis, who earlier endorsed the candidacy of Florida Sen. Marco Rubio.

It's a startling and revealing sign of the still developing relationship between Trump and Capitol Hill lawmakers of his own party, very few of whom backed Trump officially before he became the last Republican standing in the nomination fight. They want to win, but they aren't sure Trump can do it. And if he goes down, they don't want to be collateral damage.

At a private fundraiser recently, Arizona Sen. John McCain (who has offered his support for the nominee but is still skipping the party's July convention in Cleveland) warned attendees of the negative impact Trump could have on his own campaign for a sixth term. "If Donald Trump is at the top of the ticket, here in Arizona, with over 30 percent of the vote being the Hispanic vote, no doubt that this may be the race of my life," McCain said in audio obtained by Politico.

Trump himself loves his name. It's been featured prominently on his hotels, on a self-styled university and on steaks. He even talks about himself in the third person when delivering stump speeches.

But for many Republican lawmakers, aligning too closely with Trump is a gamble more excruciating than any table game at Trump's casino hotels. Senators up for re-election in blue or swing states are performing a particularly artful dodge, trying to avoid appearing to reject their party's pick while separating themselves from a man who has made comments that offend their home-state constituents. New Hampshire Sen. Kelly Ayotte, for example, has said she will "support" but not endorse the GOP nominee.

Democrats, meanwhile, are loving the name Trump, even if they don't like the man who owns it. They put out press release after press release tying vulnerable House and Senate candidates to the real estate magnate, asking rhetorically whether the down-ticket candidates agree with Trump's comments about women, Muslims and Latinos. They have declared the opposition party the "Party of Trump."

Trump's pilgrimage to the Hill on Thursday didn't end in any kind of group hug or truly unified message around Trump. House Speaker Paul Ryan, for example, while lauding a meeting the two held as pleasant and productive, is still withholding his formal endorsement of Trump.

"This is a process. It takes a little time," Ryan told reporters after the meeting.

Ryan's reluctance underscores a still-simmering problem for the Republicans: their inability to unite the feuding factions of their own party. The Wisconsin lawmaker represents a classic conservative, a policy wonk who has assigned experts to develop policy papers ahead of the GOP convention this summer. He wants a clear, unambiguous conservative message, particularly on fiscal matters, and Trump's recent waffling on raising the minimum wage and taxing high-income earners could undermine that free market thesis.

Trump is also the opposite image of the low-key, intellectual Ryan. Ryan wants to establish a strong Republican brand as one of fiscal sense and personal freedom. Provocative and unashamedly self-promoting, Trump sees himself as the brand to be sold.

Trump turned out to be right in that calculation, having won not only nearly enough delegates to secure the nomination, but more primary votes than any Republican candidate in history. That remarkable success has forced Republican lawmakers to deal with him and even, on a nascent level, to work with him.

But right now, the single unifying mission the GOP has is defeating Democratic front-runner Hillary Clinton – ironically, a name commonly uttered by Republicans when they talk about their goals for the fall elections.

"I'm an advocate for Trump because I don't want a third term of an Obama administration. That's what you're going to get with Hillary Clinton," says Sen. Chuck Grassley, an Iowa Republican.

Sen. Orrin Hatch of Utah worries about the Supreme Court. "If it's another Democrat [in the White House], the court's going to be changed for generations," Hatch says in explaining his endorsement of Trump.

Adds Sen. Mike Rounds, a South Dakota Republican: "We understand right now this is a choice between Mr. Trump and Hillary Clinton, and we know which one of those we're choosing, and that's Mr. Trump. I think she'll be one of the unifiers for us in the Republican Party."

That is surely something the GOP can rally around. But is it enough? Veteran Republicans have been complaining for years that the GOP needs to be viewed as being for something, and not just as the party against Obamacare, same-sex marriage and myriad other items. Slamming Obama, after all, wasn't a successful strategy in 2012.

"Everybody seems to be, 'OK, we've got to beat her,'" says Sen. Lindsey Graham, a South Carolina Republican who says he will not vote for Trump. "I think we've got to do more than just beat her, in terms of the party." Trump, Graham says, may well have a vision for the country – but it's not necessarily something Graham says he could support.

For now, the wary relationship between Trump and Capitol Hill is building on the common goal of defeating Clinton. With Trump and Clinton as the choices, lawmakers say, there is no choice.