WASHINGTON -- By a nearly two-to-one margin, Republican voters believe free trade is bad for the U.S. economy, a shift in opinion that mirrors Democratic views and suggests trade deals could face high hurdles under a new president.

The sign of broadening resistance to globalization came in a new Wall Street Journal-NBC News Poll that showed a fraying of Republican Party orthodoxy on the economy. While 60% of respondents said they want the next president and Congress to continue cutting taxes, 32% said it's time for some tax...