But the dollar has been rising on interest rate differentials, based on tighter U.S. monetary policy versus the easier policies of central banks elsewhere, like Europe and Japan.
"Right now I think Fed policy and underlying growth are more important than these trade issues. There are a lot of unknowns," said Marc Chandler, chief currency strategist at Brown Brothers Harriman.
Chandler said the dollar could consolidate gains early in the year, but he sees it continuing to move higher. The euro could trade several percent below parity by midyear, and the greenback could continue to move up against the yen. He said dollar/yen could reach 125.
The dollar index is up about 8 percent in the past six months, but it's gained nearly 6 percent since the election on Nov. 8.
Taxes and trade issues are expected to be high on the agenda after Trump is sworn into office on Jan. 20. The House tax proposal includes cutting the corporate tax rate to 20 percent from 35 percent, and it would rely on the border-adjusted tax to replace some of the revenue.
"The market is betting on a very broad-based increase in growth and if his policy mix actually ends up in a lumpy distribution of growth, it's not going to be positive," said Boris Schlossberg, managing director, foreign exchange strategy, at BK Asset Management.
He is looking for a higher dollar, and sees the euro below parity and dollar/yen at 125 and possible sharply lower levels of 135.
"It's difficult to predict because you don't know what Trump will do. He is very unpredictable," said Schlossberg. "He's inheriting a very strong economy, and he's got a lot of wind at his back. It's just a question of how he's going to manage it."
Supporters of the border-adjusted "destination tax" say it would encourage more U.S. production of goods and create U.S. jobs. But opponents say it will send prices higher, unfairly cut profits for some sectors, particularly the retail industry, and could prompt retaliation. The idea is similar but not quite like a VAT, or value-added tax, common in other countries.
"Proponents of the new plan, as part of the 'Better Way' reforms, such as House Ways and Means Committee Chair (Kevin) Brady, see this as a plausible addition to the tax code and WTO compliant. It's probably going to happen, so investors need to think about the market impacts," wrote Citigroup strategists in a recent note.
Others, like Goldman Sachs economics team, put lower 1-in-3 odds on the proposal becoming part of a new corporate tax code. Supporters count on a rising dollar to mute the impact of increasing costs, but strategists disagree on how much the dollar would actually rise.
The Citi strategists said it is possible, in theory, that the dollar could climb another 20 percent if that aspect of the tax plan was approved. But they added that other countries, like China, would probably intervene to support their currency, so the gain is not likely to be that great.
"Our template currently is the 1980-85 period when the currency appreciated over 50 percent albeit from a more undervalued base," they wrote.
The Citi strategists said in their recent note that the cross-border tax is another reason to be bullish on the dollar. Other positives for the greenback include the expected repatriation of billions of dollars held by U.S. corporations overseas. Trump and the House tax proposal would grant a tax break for companies to return their overseas earnings to the U.S.
"We now think the downside risks on EUR/$ could extend to 90c (and) on $/JPY to 125," the Citi strategists wrote. The euro was at $1.0392 against the dollar, and dollar/yen was at 117.61 in New York trading Wednesday.
The border-adjustment tax would depend on a stronger dollar to keep the plan from hurting the economy. "If you don't get the dollar adjustment, you're going to get the inflation from higher costs," said Daniel Clifton, chief policy strategist at Strategas.
"There's a lot of people rumbling about a stronger dollar, and for this to work it's got to adjust," said Clifton. "The retailers will get clobbered if there's not an adjustment."
Some strategists see the same border-adjustment tax proposal as a potential negative for the dollar. Other trade actions are still largely unknown, but they could also cause the dollar to stumble if they are viewed as protectionist and trigger retaliatory reactions, according to strategists.
"I don't see the logic of why it would be good for the dollar. I don't see the logic of taxing imports is good for the dollar. It could boost inflation which would make the Fed more likely to hike," Chandler said.
Daniel Katzive, head of BNP Paribas foreign exchange strategy for North America, expects a dollar correction early in the year, and he said a catalyst could be a number of things including the new administration's trade policy.
The dollar may not react positively to the proposed border-adjustment tax. "That depends on what the rest of the world does in response. Basically things that are bad for the risk environment or bad for the equities market are going to be bad for the dollar. One thing that could derail that is a risk-off period," he said. Katzive, however, said he is constructive on the dollar, and he does see the euro reaching parity next year.
He said the currency market will be watching the timing and success of implementation of the Trump corporate tax breaks and stimulus proposals, which are positives for the dollar. Trump's plans to ramp up infrastructure spending and to cut both corporate and individual tax rates has contributed to the 5 percent gain in the dollar index since Election Day.
"The tricky thing is how much of a correction do we get and when. I think it will happen in Q1," he said. Katzive said it could be due to a disruption in the risk environment, or a downgrading in Fed expectations. The U.S. central bank currently forecasts three rate hikes for next year, and many economists see just two hikes.
"You'll have a period of time when the market loses faith in the dollar trend," Katzive said. He expects the dollar to basically trade flat against the euro and yen in the first quarter.
Chandler said the euro could face political head winds. He said Europe has several important elections in the Netherlands, France and elsewhere, and gains by populists would be euro negative. Germans go to the polls later in the year.
"The nationalism is like an acid that eats away at the glue that holds Europe together," said Chandler. The dollar would surge against the euro, for instance, if Marine Le Pen wins in the French election this spring, he said.
The dollar has been rising with equities, which are up on the Trump trade, he said. "We have bid up stocks. This is tax breaks. This is less regulation. They think Trump is better for business," he said.
An inward-looking U.S. could also impact the dollar. "If the U.S. gives up being a global leader, in the short term, it's good for the U.S. In the long run, it's probably not," Chandler said.