What are the bad consequences of such an action, on a personal level and in general, if there are any?
No, this is not considered to be a sin, because Islamic says that personal conviction has its role to play in marriage. (A woman may not like a man because of something in his appearance, and she is not sinning if she refuses his offer of marriage), but if you fear that you may miss the boat or that you may not receive a similar offer, then put your feelings aside, use your common sense and hasten to get married.
From the answer of Shaykh Ibraaheem al-Khudayri.
If a woman follows her whims and desires by rejecting a man who is religiously-committed and has a good attitude, she may be punished by remaining a spinster (i.e., unmarried).
May Allaah bless our Prophet Muhammad.
Sheikh Muhammed Salih Al-Munajjid