National Indigent Women's Abortion Trust Fund Checkoff Act of 1985 - Title I: Amendments to Internal Revenue Code of 1954 - Amends the Internal Revenue Code to permit every individual with a tax liability of one dollar or more to designate one dollar of the taxpayer's income tax payment to be paid over to the National Indigent Women's Abortion Trust Fund. Permits each spouse on a joint return to designate that one dollar be paid over to such Fund.

Establishes in the Treasury the National Indigent Women's Abortion Trust Fund. Transfers to the Fund amounts designated each year for payment to such Fund. Provides that amounts in the trust fund shall be available to pay the Federal share of the cost of medical assistance for abortions under the Social Security Act.

Title II: Medicaid Amendments - Amends title XIX (Medicaid) of the Social Security Act to provide that State plans for medical assistance are required to provide for abortions in the same manner as other pregnancy-related services. Makes this requirement applicable to calendar quarters beginning on or after October 1, 1985. Provides that where a State plan requires State legislative action to meet this requirement, the plan will not be deemed to have failed to meet the requirement until the first day of the first calendar quarter beginning after the close of the first regular session of the State legislature that begins after the enactment of this Act.

Authorizes the Secretary of Health and Human Services to make payments to the States from the National Indigent Women's Abortion Trust Fund. Provides that payments from such Fund shall be governed by regulations promulgated by the Secretary of Health and Human Services.