Gary Becker and Richard Posner are not very worried by the Employee Free Choice Act

Posner says:

I doubt that the Act would have a great effect on unionization. Unions have been in steady decline in the private sector for decades and now account for only about 7 percent of nonfarm workers in that sector (farm workers are not covered by the National Labor Relations Act). Elaborate government regulation of workplace safety and health has reduced the value of unions to workers, as has greater job mobility and the increasingly technical and individualized character of many jobs, which makes it difficult for workers to agree on the terms and conditions of employment that they should be seeking. International competition has reduced the power of unions to extract supracompetitive wages, benefits, or work rules, as has the deregulation movement, which has made the formerly regulated industries, such as transportation, more competitive. Unions have little power in a competitive industry, because a supracompetitive wage, by increasing the employer's cost, will shift his output to competitors. We are seeing this happen in the automobile industry, where union intransigence has been a factor in the decline of the Detroit automakers, now on federal life support.

Becker writes:

From the 1930s to the 1960s, unions enjoyed considerable popularity in public opinion. I remember being surprised when a graduate student to hear the arguments by Milton Friedman and some of my other teachers that unions were often monopolies that benefited their members at the expense mainly of other workers. As various arguments hostile to unions became more common during the past half-century, public opinion shifted against unions. Unions are considered too selfish, sometimes corrupt, as with the well-publicized troubles of the teamsters union, and they are no longer believed considered necessary to protect employee interests.

Given this radical shift in public opinion, and the fundamental economic and social forces that contributed to the decline of unions, it is unlikely that the new Congress and new President would push for radical pro-union legislation, despite the impressive victory in the past election of the Democratic Party, and the strong financial and other support the larger unions gave to this party.