How hard do early-career academics in the United States work, really?
TL; DR: 51 work hours a week with 12 vacation days a year
It is very difficult to assess how hard someone works. It is relatively easy to quantify the input (number of hours worked and the number of vacation days taken) and the output (papers and grants). In 2003 the Sigma Xi post doc society in the US began collecting data from 7600 post docs across 46 different US institutes about a number of issues including hours worked, vacation days taken, papers published and grants submitted. A summary report Doctors without Orders is available. Aggregate data is available via the Wayback Machine. I believe this is the best data set available to answer questions regarding the input and output.
The self reports suggest 12 days of vacation a year and 51 hours a week on average with 25% taking less than 7 days and working over 60 hours. The self report of the publication rate is around 3 with one grant application.
While self reports of hours work and publications are potentially biased, they might be a better measure of the perceived "hardness" of work than the actual hours worked. Obviously it would be nice if the publication and work rates were objectively verified. Obviously, publication rate and hours worked may not be the best metrics of how hard someone is working. This study found that alcohol consumption was negatively correlated with output. It is not clear if high alcohol consumption is positively or negatively correlated with how hard one works, but it might be relevant. Finally, Forbes has a report that University professors have the least stressful job, so maybe despite the hours, we don't actually work that "hard".
The comments to the questions suggest that understanding the input/output function would be desirable. This should be possible from the raw data of the Sigma Xi study, but not from the aggregate data, to determine if the inputs (hours worked) predict the outputs (papers and grants). I would be surprised if there was not a strong correlation, but also wouldn't be surprised if there were a number of outliers (i.e., lots of input and little output and little input and lots of output). Now, publication rate may not be the best measure of output as it doesn't consider quality. A psychology study found that impact factor is not correlated with publication rate suggesting that quantity and quality, as dubiously assessed by impact factor, are not correlated.
Why is this question being singled out for a higher standard of "statistical" reasoning than any other post on this site? I offer my experiences as an early career engineering professor in the US as "anecdotal" evidence, and do so with at least as much credibility as respondents on an anonymous survey.
In my experience, it's not at all about how "hard" you work (i.e., the number of hours per week) - it is about what you accomplish. In my first year as an academic I attended 7 conferences, authored or coauthored 4 journal articles, wrote three NSF grants (one of them successful), began projects with 2 grad students (both of whom eventually graduated with PhDs), taught three classes (two of them new to me) and served on the curriculum committee. That's the kind of involvement you should be expecting. With that said, nobody is going to look at how many days of vacation you take, how many hikes you take in the mountains, or how many times you spend an extra day or two at a conference location exploring the area. It is about managing your time effectively and accomplishing things (that will appear on your CV). Finally, the day of truth arrives at the tenure decision, and no one will care about weekends or vacations: but about your contributions to the field (papers, conferences, grants) and academic reputation (as evidenced in your letters of recommendation).
As for the sabbatical question, it is not a vacation. Most academics who take sabbatical go to another institution (industry or University or lab) and work with new people in an effort to learn about new things. Sure, there are fewer responsibilities (no teaching, no committees) and fewer distractions, but this is why it works! The last sabbatical I had, I finished writing a book and entered a new research field (helped by my new colleague-friends). At my school we have a laughable method of oversight: at the start of a sabbatical one writes a two or three page description of what the planned activities are and why they are beneficial to the researcher and the school. At the end of the sabbatical, one writes a two or three page summary of what has been accomplished. As a whole, professors are self-motivated, love their work, and care about the intellectual legacy (the works, students, and influence) that they leave behind. Sabbatical is an effective way of getting out of ruts, of opening new doors, and of expanding knowledge.
I would like to put StrongBad's instructive answer somewhat into perspective.
In a survey*, 55 percent of newly hired faculty (tenure-track) at a large regional university in the U.S. called the present year the busiest of their life. These faculty members were also asked to self-assess their weekly working time. They estimated a mean of almost 60 hours per week, not very much above the finding reported in StrongBad's answer.
However, when the same persons were asked to keep record every fifteen minutes of whether or not they were doing productive work, they recorded a mean of some 30 hours per week. (This probably excluded things like writing emails or taking phone-calls, but it expressly included teaching with preparation and grading, office hours, committee meetings, scholarly reading and writing.)
This is not to suggest that these scientist were hypocritical; they probably felt overworked most of the time. The divergence between reported and actual working-time could be due to the social expectation, possibly more entrenched in the US than in Sweden, that scientists must be "hardworking", or due to biased self-perception grounded in a high stress-level, or both.
From this, one may take the practical lesson that it is extremely important both for sanity and productivity to separate work from recreation and "having a life". As to the OP's primary question, early career academics in the U.S. do work hard, but there is a difference between working hard, working long hours, and working productively; moreover, at some point, the former and the latter may be inversely correlated.
*Boyce, R (1989). Procrastination, busyness and bingeing, in: Behaviour Research Therapy 27(6), 605-611. (PubMed link)