Justices declined to hear an appeal from Oklahoma officials on pre-abortion ultrasounds.
Eleven of 14 GOP senators facing reelection support legislation to ban abortions after 20 weeks.
Abortion rights groups praised the dismissal and blasted the original Oklahoma law.
Abortion rights groups want justices to block a law that could stop services at many clinics.
Graham dismissed an assertion he is leading the effort to shore up his conservative base.
Rep. Chris Smith (R-N.J.) and 70 other members of the House proposed legislation Wednesday that would require health plans offered on ObamaCare's insurance exchanges to disclose whether they provide abortion coverage.
Sponsors of the Abortion Insurance Disclosure Act, H.R. 3279, say the bill is needed because many plans are expected to impose a surcharge for abortion coverage. While people who oppose abortion would not want to pay that surcharge, Smith expects this fee to be hidden in the fine print.
In a lengthy interview with a Catholic journal, Pope Francis dismissed the criticism he has faced from some church conservatives for not putting a strong focus on social issues, like abortion and gay marriage, during his time as pontiff. Francis said during the interview that the church must focus on a broad religious message and not simply a handful of moral doctrines.
Voters believe later term abortions should be legal when asked about specific cases in which they might occur, such as severe fetal abnormality or a long-term threat to the woman's health, according to a new poll.
Sixty-six percent believe abortions should be legal after 20 weeks if the woman would "suffer serious long-term health problems" from a full-term pregnancy, according to the survey commissioned by Planned Parenthood.
Another 61 percent said the procedures should be legal in cases when the fetus is not viable, or when the pregnancy is a result of rape or incest.
A federal appeals court on Thursday struck down Arizona's attempt to cut Planned Parenthood out of its Medicaid program.
The 9th Circuit Court of Appeals upheld a lower court's ruling against Arizona, which had sought to cut Planned Parenthood out of its Medicaid program because it provides abortions.
Critics of the contraception mandate in President Obama's healthcare law said they will appeal to the Supreme Court after a federal appeals court declined to re-hear their case Wednesday.
Alliance for Defending Freedom, one of the organizations challenging the contraception mandate in the courts, said it will ask the Supreme Court to consider whether the mandate is unconstitutional.
The case in question was filed by the owners of Conestoga, a cabinet-making company. A three-judge panel of the 3rd Circuit Court of Appeals ruled last month that the owners could not challenge the contraception mandate.