Federal budget cuts will affect social security benefits.

Literal

Federal-government [possessive-の] budget-cuts [topic-は] social-security [possessive-の] benefits [to-に] impact [subject-が] reach [conjecture-でしょう].

連邦政府の予算削減 ('federal government budget cuts'). 社会保障の給付 ('social security benefits'). 影響が及ぶ ('impact reaches') is a formal expression. ~でしょう adds conjecture.