Anzalone Liszt Grove Research has a very encouraging report on trends in public opinion favoring organized labor’s future. From their recent e-blast on the topic:

…Six years ago, popular support for labor unions hit an all-time low with only 48% approval and 45% disapproval, according to Gallup which has been tracking attitudes towards labor for nearly 80 years.
But popular support for labor unions is returning to pre-recession levels. Just last month, Gallup released a poll announcing that labor unions are enjoying an approval rating of 58%, jumping five points over the last year and 10 points since 2009. That is in line with every Gallup poll for 70 years before the recession, which found a majority of Americans approve of labor unions (72% approve 1936 / 60% approve 2008). For the first time in more than six years, more Americans would like to see labor unions have a greater influence in the country rather than less (37% more / 35% less / 24% same). At the height of anti-labor sentiment in 2009, 42% of Americans said labor unions should have less influence while only 25% thought they should have more.
Today, union membership hovers around 11 percent – half of what it once was when data was first tracked over thirty years ago. Views are mixed on whether this decline in membership has been good for the country (45% mostly bad / 43% mostly good) but a majority of Americans believe it has been bad for working people (52% mostly bad / 40% mostly good).

Even more encouraging, young people are leading the revival of support for labor unions. As the ALG report notes, “Support among different demographics gives us a few clues. 66 percent of young adults, ages 18-34, approve of labor unions and 44 percent want them to have more influence – the highest ratings among all age groups.”
And not surprisingly, workers of color, who disproportionately experience low wages and adverse working conditions, are also strongly approving unions:

Unions also enjoy a higher margin of support among minorities, a demographic steadily growing as a share of the population. African-Americans rate labor unions the most favorably (60% favorable / 29% unfavorable) while nearly half of Hispanics view labor unions favorably (49% favorable / 32 unfavorable).

As for low-wage workers in general, the report says, “Among low earners, specifically those working full time in minimum wage jobs (earning less than $30,000 annually), labor unions have a 23 point net favorability rating (54% favorable / 31% unfavorable).”
The report goes on to document the animosity of Republican leaders toward unions, including presidential candidates, and notes,

Among the GOP field, candidates wear their union-bashing credentials as badges of honor in a regular game of Who Hates Labor Unions More. Earlier this spring, Scott Walker went so far as to compare terrorist groups like ISIS to labor demonstrators during his first term. John Kasich joked that if he were king, he “would abolish all teachers’ lounges, where they sit together and worry about ‘Woe is us.'” And Chris Christie did not mince words when he said that the American Federation of Teachers deserved a punch in the face.

Such attitudes look like a big mistake. While 57 percent of Republican poll respondents have “unfavorable” views of unions, 31 percent are “favorable,” with young, non-college and lower-income Republicans having even more favorable attitudes toward labor. The Demagogic attitudes toward labor on the part of GOP leaders are not so widely-shared by the Republican rank and file.
The report concludes by observing that Democrats continue top enjoy strong support from union households, as well-evidenced by the 2012 exit polls, which reported their overwhelming support of President Obama. Further,

Obama would have lost the popular vote in 2012 without strong support from union households – he lost non-union households on election day, with union households giving him a margin of victory. The electoral impact would have been especially felt in the union-dense Midwest. In Michigan, for example, a state Obama won by nine points (Obama 54% / Romney 45%), Obama would have run dead even with Romney if no union households voted. In Wisconsin and Ohio, similarly, union households provided the margin of victory for Obama.

— Which explains why Republican leaders hate organized labor and do everything in their power to undermine union organizing campaigns, particularly in midwest states. The Republicans’ disparage and crush unions strategy intensified dramatically under President Reagan and has continued apace under Republican administrations. The ALG report indicates that the costs of the strategy to the GOP now exceed the benefits, and that’s good for America, as well as the Democratic Party.