Yes economists do agree

And one topic on which they do agree is the case for free trade. As Gregory Mankiw has recently written in The New York Times,

Among economists, the issue is a no-brainer. Last month, I signed an open letter to John Boehner, Mitch McConnell, Nancy Pelosi and Harry Reid. I was joined by 13 other economists who have led the President’s Council of Economic Advisers, a post I held from 2003 to 2005. The group spanned every administration from Gerald Ford’s to Barack Obama’s.

We wrote, “International trade is fundamentally good for the U.S. economy, beneficial to American families over time, and consonant with our domestic priorities. That is why we support the renewal of Trade Promotion Authority (TPA) to make it possible for the United States to reach international agreements with our economic partners in Asia through the Trans-Pacific Partnership (TPP) and in Europe through the Trans-Atlantic Trade and Investment Partnership (TTIP).”

Mankiw also notes that

Politicians and pundits often recoil at imports because they destroy domestic jobs, while they applaud exports because they create jobs.

Economists respond that full employment is possible with any pattern of trade. The main issue is not the number of jobs, but which jobs. Americans should work in those industries in which we have an advantage compared with other nations, and we should import from abroad those goods that can be produced more cheaply there.

Even Paul Krugman is on board with this one,

It should be possible to emphasize to students that the level of employment is a macroeconomic issue, depending in the short run on aggregate demand and depending in the long run on the natural rate of unemployment, with microeconomic policies like tariffs having little net effect. Trade policy should be debated in terms of its impact on efficiency, not in terms of phony numbers about jobs created or lost.

Trade economist Douglas Irwin has put it

The claim that trade should be limited because imports destroy jobs has been around at least since the sixteenth century. And imports do indeed destroy jobs in certain industries: [...]

But just because imports destroy some jobs does not mean that trade reduces overall employment or harms the economy. [...]

Since trade both creates and destroys jobs, a frequently asked question is whether trade has any effect on overall employment. Unfortunately, attempts to quantify the overall employment effect of trade are I exercises in futility. This is because the impact of trade on the total number of jobs in an economy is best approximated as zero.

But perhaps Laura LaHaye puts it best

Of the false tenants of mercantilism that remain today, the most pernicious is the idea that imports reduce domestic employment. This argument is most often made by American automobile manufacturers in their claim for protection against Japanese imports. But the revenue that the exporter receives must be ultimately spent on American exports, either immediately or subsequently when American investments are liquidated.

So, one may wonder, why is it that, if economists are so much in agreement, the public and their elected representatives often so skeptical? Mankiw notes Bryan Caplan's answer,

In the case of international trade, three biases that he identifies are most salient.

The first is an anti-foreign bias. People tend to view their own country in competition with other nations and underestimate the benefits of dealing with foreigners. Yet economics teaches that international trade is not like war but can be win-win.

The second is an anti-market bias. People tend to underestimate the benefits of the market mechanism as a guide to allocating resources. Yet history has taught repeatedly that the alternative — a planned economy — works poorly.

The third is a make-work bias. People tend to underestimate the benefit from conserving on labor and thus worry that imports will destroy jobs in import-competing industries. Yet long-run economic progress comes from finding ways to reduce labor input and redeploying workers to new, growing industries.

The reaction by politicians and many commentators to international trade is an excellent case in point of Blinder's Law:

"Economists have the least influence on policy where they know the most and are most agreed; they have the most influence on policy where they know the least and disagree most vehemently.”