There are at least two kinds of jobs. One kind is where the wage is posted and known and if you are offered the job, it's take it or leave it at the posted wage. Another kind is where the wage is not explicitly posted and the prospective employee may be able to bargain with the employer over the wage. There are at least two kinds of workers. One kind is unemployed and looking for work. Another kind already has a job but is looking for something better.
Well, curiosity got the better of Bob Hall and Allen Krueger (H&K, ungated paper is here) so they went out and surveyed (probably the NSF paid a firm to have the survey done) around 1400 job acceptors to see what were the relative frequencies of the different types described above in the US labor force.
H&K found in both cases the split is fairly even. Between 22% and 54% (depending on the stringency of the definition of "knowing") knew in advance what the wage would be and that it was take it or leave it. Also, around 40% of the job acceptors reported that they could have stayed in their current jobs when they took a new one. They also find that taking a posted wage job is strongly negatively correlated with education.
With a brand new PhD in hand I thought my initial job at George Mason would be a bargaining type situation. HA. Here are a list of the things I asked for and was denied: more money, a course off, summer money, a computer (this was back in 1984), moving expenses. Once I got there, Jim Bennett found money for me to get a computer, and a couple years later Bob Tollison arrived at the Public Choice Center and hooked me up with generous summer money, but at the time I was stunned. After all I'm Scottish. We are the second greatest bargainers in the world (I have to give the honor of #1 to Moroccans)! I must have improved or made myself a more valuable commodity because ensuing jobs did involve bargaining and counter-offers.
However, one big difference was that in the GMU case I was unemployed when "bargaining" with them and in later cases I could have stayed at the job I eventually left.