WASHINGTON -- U.S. President Donald Trump's surprisingly caustic complaints about trade with Canada in recent days could be setting the stage for a broader renegotiation of the North American Free Trade Agreement than previously advertised.

Irritants like dairy, softwood lumber and drug patents could be on the table in the update to NAFTA, a far more comprehensive package than the minor tweaking the president spoke of a few weeks ago, his administration suggested Tuesday.

Trump's point man on the file explicitly linked all these individual disputes to the broader negotiation. In multiple public appearances Tuesday, Commerce Secretary Wilbur Ross emphasized that the reason lumber and dairy have erupted as irritants is they're not properly addressed in the old agreement, which he called obsolete.

Add pharmaceuticals to the list: in an interview with CTV News, Ross referred in passing to a dispute involving Canadian courts' invalidating patents, and said a good trade agreement would address such points of friction.

"Everything relates to everything else when you're trying to negotiate," Ross told a White House press briefing Tuesday.

"Think about it: If NAFTA were functioning properly, you wouldn't be having these kinds of very prickly, very unfortunate, developments back to back.... If NAFTA were negotiated properly, you wouldn't have these."

When it was pointed out that dairy and lumber aren't part of the free-trade agreement, Ross replied: "That's one of the problems."

Ross was on hand to explain why the U.S. administration had begun slapping tariffs averaging 20 per cent on softwood lumber -- the latest move in a long-standing dispute.

That led to an unusual scene. The White House's daily briefing began with exchanges about the most arcane Canadian trade issues, like stumpage fees from public land and dairy regulations that have limited imports of milk proteins.

Some U.S. reporters asked why he appeared to be picking on Canada, a close ally and neighbour. Ross replied: "They're generally a good neighbour. That doesn't mean they don't have to play by the rules."

Canadian officials voiced a theory a few days ago about all the sudden, heated rhetoric: one said it's a negotiating tactic, representative of Ross's style.

That theory appeared to gain currency Tuesday.

Ross himself used the most highly visible platform in Washington to talk about softwood lumber duties, then linked what's normally an under-the-radar issue in Washington to the broader NAFTA negotiation and fielded questions from U.S. network correspondents about it.

And the Canadian government isn't necessarily unhappy about it.

One official said the softwood element could be welcome, depending on where negotiations go. In fact, the very first thing Canada said it wanted in a new NAFTA, the day after Trump's surprise election win, was a long-term deal on lumber.

One official already has an answer ready for the Americans if they complain about Canada's supply management in dairy, which restricts imports: "The U.S. has supply management for home lumber."

The Canadian government has also been reaching out to allies throughout the U.S. Federal ministers have been fanning across the country, meeting Americans who benefit from cross-border trade.

One example of an ally is the National Association of Home Builders. The association put out a statement denouncing the lumber tariff, calculating that fears of impending tariffs had driven up wood prices and added almost US$3,600 to the cost of a typical home.

"These price hikes have negative repercussions for millions of Americans," said the group.

A diplomacy official in Barack Obama's White House, meanwhile, has some advice for the Canadian government: Speak directly to the American masses.

Brett Bruen, the former White House director of public engagement, said now's the time for Prime Minister Justin Trudeau to prove he can draw a U.S. audience, and communicate directly with the millions of people who could feel protectionism's sting.

"This issue hits home for American consumers, literally. If Canada and Trudeau are smart they will invest in underlying the direct costs that will be borne by homebuyers here," Bruen said.

"It will also provide Ottawa important leverage going into NAFTA talks. If Trump knows Trudeau can create messages that resonate with middle American consumers, he is likely to pare down his demands considerably. The next battle in the trade wars needs to be waged on the Home and Garden network."