Nursing is not for everyone- and even for people who are really called to nursing, not every specialty and position in nursing is a good fit for every nurse.
It sounds like you're in a really rough spot at work- poor staffing, management and personnel changes, and low unit morale can take it out of even the most experienced and happy-with-their specialty nurse, let alone a recent grad who is still feeling their way in to their role. It sounds like you really need to get out of there, and who knows- cardiac stepdown may turn out to be a better fit. Just getting out of the toxic environment of your current unit may be a big help.
If it isn't (or if your gut overtakes you and you decide against taking the job), I would think really hard about what you consider to be the "good" and the "bad" parts of nursing before your next job search. There are SO many different kinds of jobs available in nursing, especially if going back to school is on the table for you. Do you enjoy clinical procedures but dislike dealing with patient families? Maybe OR would be a better fit. Do you like the teamwork/learning aspect of nursing more than bedside care? Maybe teaching or running a nursing school lab would suit you. There's case management, public health, administration, school nursing, hospice, product reps, transport, ER, outpatient procedures... so many areas of nursing that have little or nothing to do with what being a med surg hospital nurse is like.
Some paths might require you to go back to school or to work a little longer in clinical areas, but you might find that more bearable in a different unit and/or with a goal in sight beyond "changing these linens and hanging these fluids is what I will do shift after shift forever until I retire". All of these jobs will have ups and downs and no job worth doing will be stress-free, but it seems a terrible waste to abandon nursing altogether just because of a (really, really, really common) experience like a rough first year in med surg. If "I had a rough new grad year in med surg" were a merit badge, you'd see if on a lot of the experienced nurses you know.
Take some time to really think about what it is you DO like about nursing (remember, you've had ONE job in this crazy huge industry- whatever you thought nursing was really going to be like when you first started nursing school may still be out there) and what you don't like about your current job and talk to some of the older nurses you know about new paths to explore.
Feeling burned out and miserable in med surg after one year is not a certain sign that you went in to the wrong field; it's a sign that you're like most people (I know some people do love med surg and GOD BLESS THEM, seriously). There's a reason med surg units almost every where have such a high turnover rate and so many new grad slots available. I've been there, lots of people have been there. Loving med surg is a a sure sign that you were meant to be a nurse but NOT loving it does NOT mean the opposite.
I worked several years (you may remember them, they were some of the longest years ever) in med surg and although, like you, I loved my coworkers, I found that not long after the newness and challenging phase wore off, I was wretched. It's a hard job with a lot of demands and very little excitement or thanks and even with the best coworkers in the world, it can be draining.
I eventually switched to ER and am SO MUCH HAPPIER of a person. I didn't know that a job could be this much fun. It's not easy, either, but it's so much of a better fit for my personality and interests that it's like night and day. I may not work ER forever, but the difference in my satisfaction and enthusiasm for work is unbelievable from a year ago. And that's just switching hospital departments! (okay, I switched hospitals, too, but you get what I mean). Can you imagine how different it would be to be in a non-hospital or totally non-clinical role?
Basically: don't run away from nursing just because med-surg has burned you out. Take that hard-won degree and all that knowledge you've earned during this dark time and carve out a job that you do love. Good luck!