Also, as someone else noted, first year corporate work is very much up and down and it is typical to be less than fully occupied your first year. I wouldn't take that alone as a sign that you are going to get canned. But it sounds like there are some clear signs not just that there are going to be layoffs but that you in particular are under consideration -- I will assume that is true and that you aren't overreacting. And, quite frankly, the market for corporate work is extremely hot right now -- it has been for awhile and seems like it will continue to be for the near future. If your firm is so slow in this market, you might be better off getting out sooner rather than later.
With layoffs and terminations, many biglaw firms will give you 3-6 months to actually leave. That gives you some time to search for a job without looking like someone who is unemployed. If they do boot you right away, some severance can be expected. Since you have no debt and decent savings, it might not be a bad course of action to wait and see. The layoff fear could pass, and you'd be fine. Or it could come to fruition and you can deal with it then, when you have the facts. Regardless, in the meantime, you should use this extra downtime you have now proactively, maybe to get your resume and LinkedIn polished, to stay in touch with your contacts, or to try to increase your visibility through writing opportunities and networking events.
If you do need to jump ship....
Are you flexible on geographies? If you are in a Detroit-sized market in the midwest and biglaw firms need to do layoffs, the odds are that there are not a lot of other big firms in town that could absorb a ton of laid off associates. So if you aren't flexible geographically, it may make sense to start looking into those other local options sooner, rather than later.
Nationally, there is an extremely hot lateral market for corporate associates at all levels -- even entry level associates with no experience. They will often advertise wanting 2-4 years of experience, but the reality is that they are, out of necessity, considering and hiring first years. Think about whether and under what circumstances you're willing to move.
At your level, I don't think a recruiter will add much value. In fact, they may well hurt your chances since a firm will need to budget in paying their recruiter fee.
As you apply for other opportunities, be thoughtful about the process. Secondary markets at the midwest are thin, and if you get "dinged" with a half-assed application sent to the recruiting people, you may not get a second chance. So don't carpet bomb resumes, and pursuing leads into firms that don't just go to the recruiting email. You're much more likely to get noticed -- and less likely to get permanently dinged -- if you, say, get your law school buddy to set you up with coffee with the partner who does lateral hiring or the head of the corporate group to casually "discuss opportunities" rather than applying. It's kind of like a freebie screener interview.