The U.S. government has published its 2013 Poverty Guidelines. If you are sponsoring a family-member immigrant for U.S. lawful permanent residence (a green card), you will need to fill out a USCIS Form I-864 on the immigrant's behalf.
That means you will need to show that, according to the numbers set by the Poverty Guidelines, your household income is high enough to serve as a sponsor for the immigrant(s) at an amount 125% of more of U.S. poverty levels, thus making sure that he or she does not have to rely on need-based public assistance (welfare) in the United States. You will also have to be able to support anyone else dependent upon you. To view and download the 2013 Poverty Guidelines, go to the USCIS website at http://www.uscis.gov/files/form/i-864p.pdf.
For more information on the petitioner’s role as financial sponsor, see Nolo’s articles on “The U.S. Sponsor's Financial Responsibilities.”