“Elbows Up,” a hockey phrase, became the campaign rallying cry of Canada’s Liberal Party this spring, whipping up a swell of patriotism in the face of President Trump’s menacing posture toward America’s neighbor.

In April, the sentiment lifted Mark Carney, a prominent economist but neophyte politician, to one of the most stunning electoral victories in Canada’s history. He promised to fight back against American tariffs and stand up for Canadian sovereignty.

But, after just a few months on the job, Mr. Carney is facing early signs of trouble as he discovers that being elected on an anti-Trump message does not mean you can govern on one, too.

Since taking office, Mr. Carney has tried to hone a firm-but-friendly tone in his interactions with Mr. Trump. In two high-stakes in-person meetings, he avoided any missteps in dealing with the American president, who has repeatedly said he wanted to make Canada a part of the United States and has slapped tariffs on key Canadian goods.

Yet, so far, Mr. Carney’s pleasant relationship with Mr. Trump has yielded little that’s tangible for Canada.

Unlike the European Union and Japan, Mr. Carney has not been able to deliver a trade deal with Mr. Trump, who ignored mutually agreed deadlines during the summer to come up with one.