LuoXiaoye:
Yes, the expression "The---Clock's---Ticking" does mean that time is running low.
In this context, it refers to the woman thinking that the years of her life, in which she is eligible to be married, are rapidly passing away. After that, she can expect to be "On Old Maid" which is to say, an unmarried woman.
"Sweep----Me---Off---My---Feet" means that the woman has encountered a person (Romantic Interest) or a situation in which she is emotionally overwhelmed.
In this movie, it would mean that the woman met a man that was well--dressed, refined in manners, charming, and appeared to be financially well-off. In other words, she met what is called a DREAMBOAT.
When that occurs, all of her normal resistance to the man vanishes, and vulnerable to agree to any invitation to date, and she probably feels totally out of control.
In celebrity culture, one may suppose that
Justin Bieber would exemplify that kind of Dreamboat who would sweep a woman off her feet.
As a man, I don't think much of him, but I do not see him as others do.