But like most aspects of the abortion debate, it is controversial.
Some doctors argue about when a fetus has the nerve growth to feel pain, with estimates ranging from 20 to 28 weeks of gestation.
D.C.'s nonvoting House delegate Eleanor Holmes Norton slammed Lee's bill. Sidestepping the medical argument, she accused Lee of pushing a test case for a nationwide campaign for more restrictive abortion laws at the expense of local control.
"Senator Lee is trying to undemocratically usurp local authority outside his own state in violation of every founding principle of local control," she said. "And at the same time to introduce the idea that basic constitutional rights depend on where a citizen lives."
Norton said she would urge pro-abortion rights groups to fight Lee's bill and a similar piece of legislation in the House.
Lee called Norton's claims "absurd" and defended his focus on the nation's capital, which Congress directly oversees.
He said he would oppose a national version of his legislation, arguing that states should make such laws.
"I don't believe Congress has the authority to tell the states what they can and cannot prohibit to allow in this area," he said.
Lee would like to see Utah's Legislature adopt a similar law, saying he thinks it is "good policy," though he said that's a decision left up to state lawmakers. So far, in the middle of the state's 2012 session, no state lawmaker has introduced such a bill.