The answer to your question is: Probably not, but maybe if you get lucky.
If I understand the situation correctly, you're currently here doing an interventional fellowship but did no prior training in the US, and I'll assume not in Canada. If your prior training was in Canada, then the answer is completely different as canadian and US training is considered equivalent.
1. You can't "adjust" your visa status. J visas require that you return to your home country (whichever one generated the Letter of Need for your J visa) for 2 years before you can get any work/immigration visa here in the US. Even if you were to marry a US citizen, you can't get a GC because of your J visa. But there is one exception:
2. You can work for a J Waiver position. Each state gets 30 total positions each year. Your employer needs to certify that a US citizen was unable to be found to fill the position. I don't know whether Interventional Cardiology has unfilled spots, nor whether states will be willing to use their J waivers for them. But you have two other problems:
3. Most states require that IMG's have 3 years of GME experience in order to get a license. Interventional Cards is either 1 or 2 years depending on the program. Not all states have the same rules, you'll need to check. But if you don't qualify for a license, you can't work. The Board of Medicine can give you a license as an exception, but you (and likely your employer) will need to petition them and this will certainly delay the hiring process. But the BOM could simply refuse, and many will.
4. You will also not be Board Certified. In order to Board Certify in IC, you'd need to be BC's in Cardiology, which requires BC in Internal Medicine. Your foreign training will not count towards any of those. There is, again, one exception pathway -- if you're sponsored by a Department of Medicine you can ask for an exception, but usually this is for exceptional candidates -- i.e. some field leader from another country comes to the US, they can get Board Certified. I doubt this will qualify you.
So, short answer. You probably can't stay. You'd need a J waiver position, a medical license without enough GME experience, and Board Certification.
But, there's always a chance. You might be able to find a position that can offer you a J waiver, and that doesn't require board certification, and in a state that requires less than 3 years of GME experience or that's willing to make an exception to grant you a license. But finding that combination is not going to be easy.
