Lee's measure says Congress should prohibit abortions in D.C. after 20 weeks of pregnancy except when a woman's life is threatened.
The resolution defends the move as a reasonable extension of lawmakers' constitutional authority over the District. It suggests that doctors who disobey the ban should be imprisoned for up to two years.
D.C.'s representative in Congress called the measure a ploy to overturn Roe v. Wade and pressed senators to reject it.
"Sen. Lee, a Tea Party leader, professes to believe in states' rights and local control of local affairs," said Del. Eleanor Holmes Norton (D) in a statement. "His actions suggest otherwise."
Debates over abortion in D.C. have long pitted conservatives against supporters of home rule. Opponents of abortion rights say the District's laws are too liberal, while abortion rights supporters say Congress should not meddle in D.C.'s affairs.
Norton said NARAL Pro-Choice America has agreed to score a vote on the amendment if it comes to the Senate floor.
The chamber could start a series of budget votes on Friday night.