In a breach of bedrock conservative principles, House Speaker John A. Boehner laid out a proposal Tuesday to allow tax rates to rise for Americans making more than $1 million a year.

And standing side by side with Boehner as he outlined what many Republicans consider an apostasy — but what Boehner argues is the only way to spare most people from a tax increase — was House Majority Leader Eric Cantor, who has worked hard in recent months to play the loyal lieutenant.

“The Democrats have one negotiator: the president. And we have one negotiator, and that’s the speaker,” Cantor (Va.) told colleagues at a GOP meeting at the Capitol last week, urging them to unite behind Boehner (Ohio) in the talks.

In the “fiscal cliff” drama, Cantor has been casting himself as a supportive bit player to Boehner, a contrast from the debt-ceiling showdown of 2011. At that time, Cantor had a starring role as a lead negotiator in high-level talks with Vice President Biden and as a chief antagonist to Obama, tangling with the president in one tense White House exchange.

But that role did not go well for Cantor. It neither strengthened the GOP’s hand in the fiscal crisis nor served the lawmaker’s image. He emerged with a taint of disloyalty toward Boehner and a new reputation, carefully stoked by Democrats, as the leader of hard-liners unwilling to compromise.

Now, Cantor is serving as the loyal lieutenant. First Boehner, then Cantor argued emphatically to fellow Republicans: If Republicans do nothing, taxes are scheduled to rise for all Americans at the end of the month, and the GOP’s goal must be to shield as many Americans as possible.

Even as Boehner continues negotiations with the White House on a broader deficit-reduction deal, Cantor said he would schedule a vote on Boehner’s new alternative to spare more than 99 percent of Americans of a tax increase.

Cantor’s role has been scaled back this time, in part by the White House, where officials have made clear that Obama thinks a deal with House Republicans would have to be reached directly between himself and the speaker.

But Cantor’s strategy also was designed to show unity among top House Republicans, in contrast to last summer, when the GOP was plagued by rumors — which aides insist were overstated — of tension between Cantor and Boehner.

“That’s bad for any majority leader,” said Rep. Mike Simpson (R-Idaho), one of a group of Boehner allies who warned the speaker during the debt-ceiling talks that Cantor could move against him if Boehner accepted a “grand bargain” on deficit reduction that conceded too much. “You elect a team. The rest of the conference expects them to work together. And if the perception out there is that one is kind of nipping at the heels of the other, it’s not good for the leadership team.”

“ ‘Be careful,’ ” Simpson said he told Boehner then.

In the months after the debt talks, Democrats chose Cantor as a useful campaign foil, frequently labeling him as the face of Republican obstruction.The barbs angered Cantor’s allies, who said Democrats and the media treated him unfairly for making a principled stand in favor of spending cuts.

Even so, Cantor has tried to soften his tone since the debt fight, shifting his attention this year to a handful of bipartisan legislative priorities that had a chance of passing even in an overheated campaign year, including a measure to clarify insider trading rules by lawmakers.

In an effort to improve his image last year, he invited “60 Minutes” to interview him — along with his wife, mother-in-law and son — at his Richmond home.

And he stopped holding a weekly gaggle with print reporters, an event that often resulted in a day of Cantor headlines. Now his appearances on the Hill are more often limited to those in which he is at Boehner’s side.

His off-the-radar role this time has come partly because of a change in dynamics from the White House. Neither Cantor nor Biden was included in a Nov. 16 meeting at the White House between Obama and congressional leaders that began this round of negotiations.

Cantor and Biden have a friendly relationship and have met since the November election, but their talk was limited to breaking a partisan impasse over the reauthorization of the Violence Against Women Act, not the fiscal debate, an aide said. Each of Obama’s one-on-one meetings and phone calls since November have been with Boehner alone.

Cantor’s aides insist that despite his low public profile in the current talks, he has been deeply involved at each step as an adviser to Boehner.

He is the only House member to hold a one-on-one meeting each week with the speaker.

He also participates in a daily strategy session with Boehner, House Majority Whip Kevin McCarthy (R-Calif.) and top committee chairmen.

And when Treasury Secretary Timothy F. Geithner came to the Hill on Nov. 29 to deliver a White House proposal that included $1.6 trillion in new revenue, he met jointly with Boehner and Cantor.

“Just because he’s not in meetings with the president doesn’t mean he’s not involved,” a Cantor aide said.

Cantor’s allies also bristle at questions about his ambitions, a favorite Washington guessing game that sometimes creates the impression that he cares more about getting his next job than doing the one he has now.

His friends note that at 49, he has plenty of time to consider other prospects, including succeeding Boehner, 63, as speaker.

“I get annoyed that we’re never allowed to do what we’re doing because it’s right,” said Ray Allen Jr., a top political adviser. “He is the first Jewish majority leader in history. It’s the first time since the founding generation that a Virginian is in charge of anything in Washington. . . . He has an important job to do, and it’s a job he takes seriously.”

The best thing for Cantor’s political future may be to be remembered as a loyal soldier to Boehner in difficult talks that left Republicans with many bad options and little leverage, said Rep. H. Morgan Griffith (R-Va.), who has known Cantor since the two served together in the Virginia legislature in the 1990s.

“Being successful as majority leader means that everything’s running well, that it’s a well-oiled operation on the floor, and that things are going well,” he said. “Undermining the speaker is not being a successful majority leader.”

Simpson said he has come to believe that the problems from the 2011 debt-ceiling debate stemmed more from clashes between the two men’s staffs, which have eased. There have been staff shake-ups in both offices and a joint summit in January designed to fix problems.

“I see more unity between them, which I think is good,” Simpson said. “It’s good for our conference. Both of them realize that.”

If the speaker reaches a difficult deal with Obama in coming days that includes a tax rate increase, Cantor’s support could provide key cover for Boehner among conservatives. His support also probably helped to soothe concerns Tuesday about a possible Republican alternative that would also allow tax rates to rise.

For now, both men have worked hard to portray a common front, both in public and in private.

The day after the election, Boehner delivered a major address, indicating for the first time that he was willing to include higher revenue from limiting deductions and closing loopholes in a deficit reduction deal, a significant change of position for the GOP. Cantor quickly issued a statement of support.

“I stand with Speaker Boehner when he says, ‘Let’s rise above the dysfunction, and do the right thing together for our country,’ ” he said.

Paul Kane contributed to this report.