"We have [the dollar] going higher, but I think it's clearly going to be anything but a straight line, as today illustrates. There will be significant interruptions to that trend," said Adam Cole, head of G-10 foreign exchange strategy at RBC.
Cole said the new administration's comments will certainly have an impact on the currency market, but the White House will gradually lose its ability to jawbone the market as time goes on.
"I think they have the most value when they have novelty value, as they do with a new administration. We're at the early stages of figuring out what the administration means," he said.
German Chancellor Angela Merkel on Tuesday rejected Navarro's claim that Germany was using an "undervalued" euro to gain an advantage and said that her government has always relied on the European Central Bank to pursue an independent policy.
Navarro, last week on CNBC, also criticized Germany for its VAT tax.
"Germany — one of the worst actors in the international environment, when it comes to the [value-added tax] because what they've done is strategically raise that to 20 percent. Whereas Japan is much lower. They're sticking it to us. When they send us a BMW or Porsche into our markets, they basically rebate the VAT to those manufacturers like a subsidy and if we try to sell them a Ford or a Chevy, they slap on the VAT. That's not going to happen under a Trump administration," Navarro said.
Cole does not expect the comments to lead to a protectionist trade war, at this point.
"Particularly, for some of the developed countries — Japan, the euro zone and Germany—there isn't a huge amount they can do without taking the huge step of imposing bilateral tariffs or something as draconian as that. We think we're a long way from that," he said.
But the jawboning is new from the United States. "It is a regime shift compared to what we've been used to for many years," he said.
Chandler too said it will take some months to see what the Trump administration does.
"I don't think people are going to change their forecasts based on a dozen comments ... The market is trying to wrestle with these new developments, but ultimately policy is what dictates the currency prices. We have to wait and see. If there is deregulation, tax cuts and infrastructure spending, as well as some protectionism, like a border tax, I don't like it but I could see how it could be good in the short run for the U.S. economy," said Chandler.
The controversial border tax is not given high odds of gaining approval, but it was proposed by a House committee and is favored by Navarro. The border-adjusted tax would tax all imports coming into the country but not exports, so it could be viewed negatively by trade partners, even if those nations already have a VAT.
Supporters say it would lead to more U.S. manufacturing and jobs. But the policy needs a strong dollar to work, and some say a 25 percent appreciation would be necessary to keep the tax from harming importers and consumers. Congress proposes cutting the corporate tax rate to 20 percent, and the border tax plan is a big part of the way the tax break would be funded.
"They can't say the euro is undervalued and at the same time pursue policies that could send the dollar up another 20 percent," Chandler said.