Sen. Mark R. Warner (D-Va.) talks to members of the media before an election night event in support of Terry McAuliffe at the Sheraton in Tysons Corner on Nov. 5 (Toni L. Sandys/The Washington Post)

Despite sweeping losses in this month’s off-year elections, Virginia Republicans are hoping that the botched rollout of the health-care law will drag down Democrats across the country in 2014 — including U.S. Sen. Mark R. Warner.

But if Republicans want revenge after their drubbing by Democrats this year, they must overcome some familiar hurdles.

The first is that Warner remains extremely popular, polls show, and has the wealth to fund a formidable reelection campaign. The second is that Republicans lack a big-name candidate willing to take him on, and they may not get one as long as they stick with their plan to select a nominee at a party convention rather than in a primary.

“I don’t see a whole lot of vulnerability for Warner, and even if the environment gets pretty awful, you still need a credible candidate,” said Jennifer Duffy, who covers Senate races for the nonpartisan Cook Political Report.

Both the Cook Political Report and the nonpartisan Rothenberg Political Report rate Warner’s race as “safe” for Democrats, meaning a partisan flip is highly unlikely.

Warner, who declined to comment for this article, has long enjoyed high favorability ratings. A Quinnipiac University survey in September gave him a 61 percent job-approval score, although that was before the Affordable Care Act’s rollout began affecting the poll numbers of President Obama and the Democrats.

To some in the GOP, the answer is obvious: Virginia Attorney General Ken Cuccinelli II should pivot from his Nov. 5 gubernatorial race, which he lost by less than 3 percentage points to Terry McAuliffe (D), to a quest for the U.S. Senate. But that looks unlikely.

In mid-November, Cuccinelli told The Washington Post that he saw the race against Warner as “tempting” because of the controversy surrounding the health-care law.

“There is no such thing as an un-endangered Democrat who promised, as Mark Warner did, on video, sitting in his Senate office, ‘I would not vote for a health-care plan that doesn’t let you keep health insurance you like,’ ” Cuccinelli said. “Oh, really? You were the tie-breaking vote. . . . Mark Warner’s not going to have a cruise in 2014.”

Despite that rhetoric, Republicans who know Cuccinelli well say privately they do not expect him to run, partly because he will need the income and benefits from a full-time job to support his family after his service as attorney general ends in January.

Beyond Cuccinelli, the field appears wide open — and thin.

So far, two little-known Republicans have entered the race: Shak Hill, a Centreville financial planner, and Howie Lind, a former Pentagon official and lobbyist from McLean. Both men are military veterans who have worked on Virginia’s 10th Congressional District Republican Committee.

Neither has mounted a big-ticket campaign before or demonstrated he can raise the kind of cash necessary to keep pace with Warner.

Patrick Murphy, Lind’s campaign manager, said Lind would be competitive because “he has a deep background in defense issues, which Mark Warner lacks,” and because Warner is “one of Barack Obama’s most reliable wingmen in the Senate.”

Hill acknowledged in an interview that he was “the underdog” in the race, but he compared himself to U.S. Sens. Ted Cruz (R-Tex.) and Mike Lee (R-Utah), who both won tough primaries with support from the tea party movement.

“They were also at very low name ID when they entered their respective races,” Hill said.

Through Sept. 30, Hill had raised $118,000 — nearly all of it from his own pocket — and Lind had raised $83,000. Warner had $5.9 million in the bank as of that date.

Among better-known Republicans, Gov. Robert F. McDonnell and Lt. Gov. Bill Bolling are not expected to run. State Sen. Mark D. Obenshain (Harrisonburg) is awaiting a recount in his tight race for attorney general and probably won’t say anything more about his future until he knows the outcome of that election.

E.W. Jackson, the Chesapeake minister who lost the lieutenant governor’s race this year by a wide margin, has yet to say what he will do next.

“I am still thinking about the future, and far from ready to make any announcement at this time,” Jackson said in an e-mailed statement.

Jackson won the nomination for the post at a state party convention over six candidates who were mostly better-known and better-funded than he was. His choppy campaign and convincing loss are reason enough for some Republicans to hope that the party will hold a 2014 primary.

But at the moment, the plan is to hold a convention, and several Republicans said they saw no concerted effort within the state party to change that decision.

Stafford County Board of Supervisors Chairman Susan Stimpson, one of the GOP candidates who lost to Jackson in the lieutenant governor’s race, said primaries and conventions each have their merits. And while she’s not running, she thinks Warner can be beaten.

“I want someone to name one time Mark Warner has voted opposite what President Obama has pushed for,” Stimpson said. “I think he’s very vulnerable.”

Prince William Board of Supervisors Chairman Corey Stewart, another defeated candidate for lieutenant governor, thinks the party needs to change how it picks its nominees. “We’ve got to take a serious look at changing the nomination process to a primary. . . . There’s never been any doubt that a primary is better for choosing the most electable candidate,” Stewart said.

Stewart also says that the Republican who faces Warner “is going to have one hell of a time.”

“He’s obviously popular,” Stewart said of the incumbent. “Anything can happen . . . but I don’t think it’s likely, and whoever we nominate is going to have to be a real strong candidate to have any chance at all.”