The fiancé visa is an unusual one. Although technically it's a nonimmigrant visa (which lasts only 90 days), its purpose is not only to allow the K-1 visa holder to enter the U.S. and marry the U.S. citizen sponsor, but to allow the immigrant to apply for a green card if desired.
So, while the financial standards for most nonimmigrant (temporary) visas require simply showing that the applicant has enough money to cover his or her short stay in the United States, fiancé visa applicants must show a bit more, as discussed here.
Again because of the hybrid nature of this visa, the exact guidelines depend in part on the consular officer conducting the visa interview. Each consulate has a lot of discretion in evaluating the income needed for a fiancé visa to be approved.
Some consular officers may simply apply the "eyeball" test for fiancés—if the applicant looks young and healthy, that's enough to justify granting the K-1 fiance visa (which is, after all, good for only 90 days and comes only with the requirement that the couple marry, not that the immigrant apply for a green card—he or she can always choose to return home after the wedding).
Other officers, however, might require fiancé visa applicants to show that their sponsor is able to support them at 100% of the federal Poverty Guidelines. These guidelines are published annually and can be found on Form I-864P, published by U.S. Citizenship and Immigration Services (USCIS). The sponsor might be asked to submit an Affidavit of Support on USCIS Form I-134 (which is much shorter than the I-864 Affidavit that sponsors of immigrants for green cards must fill out).
Both the advantage and the disadvantage of the Form I-134 Affidavit of Support is that it is not considered to have much legal weight. In other words, although a U.S. government agency could take a sponsor to court to enforce it, they never seem to do so.
Perhaps they realize they wouldn't win. That's an advantage because makes it easier for the U.S. citizen fiancé to sign the form, knowing that it won't endanger his or her financial future if the marriage never happens.
It's also a disadvantage: Because the consular officials know that the affidavit is hardly worth the paper it's written on, they may disregard it and rely on other facts about the U.S. sponsor's financial condition. In most cases, though, a signed I-134 from the U.S. fiancé showing income or assets at or above 100% of the poverty level for the household size will be all that's needed.
However, the information provided on Form I-134 or otherwise will stay in the applicant's file. And, within a mere few months of arriving in the U.S., the applicant should have married and might choose to apply for a U.S. green card. So, it is to the fiancés' advantage if, at the time of the consular interview, the sponsor can show an income level at or above 125% of the minimum in the guidelines. (Showing anything less at this point may raise questions during the eventual green card interview that takes place in the United States.) In addition, some consular officers are particularly strict in dealing with fiancé visas, and will be more likely to deny the visa if the sponsor's income is not at the 125% level.
If you, as the U.S. citizen sponsor, are having trouble meeting the consulate's standards for getting your foreign-born fiancé a K-1 visa, you won't be able to have a "joint sponsor" sign an affidavit of support, the way you can when it comes time for him or her to apply for the green card.
However, if you have family members who live with you and have income or assets that could be used to support the fiancé, definitely let the consulate know about that. The best way might be for that person in your household to fill out and sign an I-134 form, with proof of income and/or assets. Although the consular officer is not required to accept the I-134, it might help convince the officer that the fiancé will be taken care of in the United States.