Odds of Getting In
Depends on what you're hoping to get into. There are already thousands of different cards out there, accumulated in the roughly one hundred years that Hallmark and other card companies have been producing them. What makes you think that your one, single, lonely card idea is original enough to merit production?
If you won't be able to move on with life until you've published your greeting card, you can up your odds by writing humor and jokes, especially self-aware jokes that poke fun at the gadget-obsessed, Facebook-addicted millennial generation. In general, though, your odds of making money are higher if you go into freelance greeting card graphic design and illustration (source).