I heard in the name of R’ Nosson Kopshitz shlita, and R’ Binyomin Garbuz shlita that strictly speaking, if one doesn’t have the money, he isn’t obligated to travel to Chutz La’aretz to find generous donors, however, if one is able to, it is fitting and correct to do so. It is no worse than all other mitzvos where one must do the appropriate hishtadlus to be able to carry it out, and it is no worse than a tzedokah fund which goes around to collect money for orphans.
However, I heard in the name of other gedolei hora’ah that it depends very much on the make-up of the father. If he is the type of person who normally does such things and is happy to go around collecting money, then he is obligated to do so, however, if he is embarrassed and scared to do such a thing, then we can’t obligate him to do so. This normally depends on who the father associates himself with, and what type of family background he has.
The Pele Yo’etz (Erech Bas) writes: One should go around collecting money, in order to be able to marry off his daughter to a talmid chocham.