This is really a two-pronged question. Your first consideration is whether a bank or other lender thinks your existing income and level of debt leave room for you to take on a home mortgage. (We're assuming you haven't saved up enough cash for the entire house purchase, but will need to take out a loan.) For information on what criteria institutional lenders use, see Nolo's article Qualifying for a Mortgage.
An important second consideration is whether, regardless of what the lender says, the expenses of a home loan -- not to mention other costs like buying furniture, dealing with home repairs and maintenance, and paying the property taxesn insurance, and utility bills -- will fit comfortably within your budget. Run your own numbers to find out, and get help from Nolo's Essential Guide to Buying Your First Home, by Ilona Bray, Alayna Schroeder, and Marcia Stewart (Nolo).
In the end, many people find that buying a home is a financial stretch -- but that the tax deductions that come with home ownership offset the expenses to a greater extent than they'd expected. For more information, see Nolo's article Rent or Buy a House?