What is the possibility of getting a green card if I am happily married to a US Citizen right now?

Generally, if a foreign national enters the U.S. lawfully and with inspection, such was with a B1/B2 visa, and later becomes married to a U.S. citizen, the couple can succeed in an adjustment of status application process by which the foreign national spouse can become a Permanent Resident (can get a "Green Card"). This is true even if the foreign national spouse may have long overstayed his/her initial visa. Of course, there are many other details that determine eligibility. It would be wise for you and your spouse to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.