Allowing Steady Savings by Eliminating Tests Act or the ASSET Act This bill prohibits the use of asset tests or resource limits in certain means-tested public assistance programs and increases the resource limits to qualify for Supplemental Security Income (SSI). SSI is a federal income supplement program designed to help aged, blind, and disabled individuals with limited income and resources meet basic needs. Under the bill, states may not use asset or resource limits to determine eligibility for (1) programs funded by Temporary Assistance for Needy Families grants, (2) the Supplemental Nutrition Assistance Program, or (3) the Low Income Home Energy Assistance Program. In addition, an individual may have up to $10,000 in certain resources (or up to $20,000 for a couple) and qualify for SSI. Under current law, the limit is $2,000 for an individual (or $3,000 for a couple).