It depends on your state's laws and the company's reputations as to how I would handle it. In many states, employers can hire and fire at will, and if the company does so, then I see it as I can come and go at will. Even in these states, some more reputable companies will give a employee notice before layoff and if I can reasonably do so, I will try and afford them that same courtesy.
If an employers insists on you accepting the job offer immediately, I would take it, but give a delayed start date if possible. They are trying to pressure you into taking a job before considering all of your options which means they are afraid of you finding a better offer elsewhere. If you had more options, but they were the best, why would they be afraid of giving you an extra week unless they really, needed someone tomorrow? I usually give a start date at least 2 weeks out. This gives me time to attend other interviews and weigh my options. I can always call back and refuse the offer and take some other one. Unethical? Maybe, but when the job market is this bad and employers are trying to game it to their favor without giving people some common courtesy, then it's them that ends up with the short stick sometimes.
That being said, there are some great employers out there and if they give you some time to review your offers, you should use that time to actually do so and accept when you are ready. Since they are giving you a week or two to consider the offer, that's another week or two they can't offer the position to someone else when they may really need help.
One company that downsized told their employees about a month and a half in advance so they would have time to find other jobs. This was a very reputable company whose owner personally told each employee that was being let go in his office of the situation. When I had to leave for some career advancement, I gave them my two weeks but offered to stay an extra 2 weeks past that if they needed me knowing they might need the help. They gladly took me up on the offer and paid me an extra $50 per diem past my two weeks for staying on to help when I could have been at home packing for my move.
On the other hand, a company that wrote me an email on a Friday afternoon saying I could do the unethical and illegal things they wanted me to do, or I could leave because "EMTs right now are a dime a dozen" got handed the "screw you" letter. I walked in 2 minutes before my shift started, handed them my resignation letter effective immediately, and started to walk out. When my supervisor told me, "Where you going? We have an ALS run pending that we need you on NOW!" I replied, "Not my problem anymore, I no longer work for this company." Boy did that feel good! I normally advocate for not burning bridges, but when paychecks have been off for 6 weeks and now you're asking me to do illegal things and jeopardizing my card, I'm leaving right now! Could I have given them the weekend to find staffing to replace me? Probably, but they didn't deserve that courtesy.