Can anyone who marries a U.S. citizen get a green card, no matter what their immigration situation might be?
Not necessarily. If a foreign national enters the U.S. legally but later became out of status due to the expiration of his or her visa or violating its terms, he or she can still obtain permanent residence based upon marriage to a U.S. citizen. However, if the person entered the U.S. without a visa and is not eligible for 245(i) by virtue of having some element of an approvable-when-filed permanent residence case on file before April 30, 2001 (see our 245(i) FAQ), then the foreign national cannot Adjust Status here in the U.S.
Part 2: Can anyone who marries a U.S. citizen get a green card, no matter what their immigration situation might be?
Even if a foreign national is in valid status, has entered legally before falling out of status, or is 245(i)-eligible, they may still not be eligible for permanent residence. Several grounds exist which may may prevent a person from getting a green card, including but not limited to certain prior criminal acts, inability to financially support oneself, health issues, or prior membership in certain organizations among other things. For some of these obstacles, waivers or other means of coping may be available, while others will serve as permanent bars and even marriage to a citizen - and even hardship to that citizen - won't help.