When President Trump addresses Congress in his first State of the Union speech on Tuesday, he will be able to plausibly claim that the first year of his presidency represented one of the most successful years for conservative domestic policy goals since the end of the Cold War. But to succeed in 2018 and beyond, the president should chart a course that returns to his roots in the 2016 campaign and breaks with the surprisingly conventional Republican nature of his policies. He has a golden opportunity to do so in the State of the Union by making a strong case for a policy few Republicans will even address publicly: paid family leave.

During the campaign, it became clear that a major part of Mr. Trump’s appeal was that he frequently broke with Republican orthodoxies on a host of issues, including foreign policy, trade, entitlements, health care and, to some degree, immigration. His unorthodoxy proved to be an asset for his campaign and is among the reasons exit polls indicated he prevailed over Hillary Clinton among independent voters.

Yet these same independents are by and large the supporters Mr. Trump has lost over the past year. Much of this is no doubt due to the tenor of this presidency and the daily barrage of tweets, leaks, investigations and general partisanship that is the hallmark of Washington these days. But his loss of support among independents may also be partly because his presidency has turned out to be much more generically Republican than what many anticipated.

President Trump’s tax cut bill, his repeal of the individual health insurance mandate, withdrawal from the Paris climate accord and rollbacks of regulations have extended Republican priorities or undone policies enacted under President Barack Obama. Republicans have every reason to be happy with the results, but Mr. Trump has yet to entertain policies no other Republican would consider — as he had once promised to do.

Mr. Trump can reach out to independent voters in 2018 by more forcefully advocating nonconservative ideas, like the oft-teased infrastructure bill, which would spend taxpayer money on a host of projects in what would almost certainly be a foolhardy way.

Less foolhardy would be paid family leave. Unlike any other industrialized nation, the United States lacks a legal guarantee of paid family leave, the absence of which places strains on many working- and middle-class families. It has long been a subject near and dear to the priorities of his daughter Ivanka but has been kept at arm’s length by congressional Republicans who loathe the idea of creating a new mandate on employers or a new taxpayer-funded entitlement, and who do not like the idea of raising taxes or cutting spending to pay for it.

Yet there is a possibility this tension is breaking. In recent weeks, an idea that was the brainchild of the Washington lawyer Kristin Shapiro has received increasing attention on Capitol Hill. As outlined by Mrs. Shapiro and the former principal deputy commissioner of Social Security, Andrew Biggs, this approach would address the main reason paid family leave has been a non-starter among Republicans in Congress. As they describe it in a recent Wall Street Journal essay, they would offer new parents the opportunity to collect early Social Security benefits for a specified period after the arrival of a child. To pay for the cost, parents would agree to delay collecting Social Security retirement benefits for another specified period shorter than the actual leave.

This idea offers an elegant solution to a difficult political problem and, according to Mr. Biggs’s calculations, could result in paid leaves equivalent in length to those offered by other industrialized nations.

At the urging of the White House, this idea has already been taken up by some Republicans in the Senate, who have been briefed on the concept and are on the cusp of drafting legislation. It is receiving early support from both conservative and moderate members of the Republican conference, and Ivanka Trump has discussed it at length with at least one — Senator Mike Lee of Utah. Support from Mr. Lee, one of the most conservative members of the party, would be crucial to passing a bill.

As Republicans work to make traditional conservatism and populist Trumpism coexist harmoniously inside their party, creativity is required to achieve compromises on policy goals. By making paid family leave a signature issue for 2018, President Trump would be embracing an idea at the heart of his 2016 success: that he is the one Republican willing to break with party norms to help working- and middle-class Americans.

If Mr. Trump can do so while bringing along conservatives wary of such steps, it is all the better for his political prospects and in keeping with his surprising ability to prevail in spite of his critics.