WASHINGTON – Efforts to convince the Senate to adopt additional restrictions on abortions, a step that has recently been taken by several states as well as the House of Representatives, look to be going nowhere despite growing pressure from Republican lawmakers.

An aide in the office of Senate Democratic Leader Harry Reid, of Nevada, who controls the flow of legislation to the floor, said the upper chamber won’t consider House-passed legislation that prohibits a woman from undergoing the procedure more than 20 weeks after conception.

Even if Reid were to consider the measure, it’s unlikely that any Senate committee of jurisdiction, all chaired by Democrats, would pass the measure on to the full chamber. President Obama already has indicated he would issue a veto if the bill reaches his desk.

Sen. Patty Murray (D-Wash.), an abortion rights supporter, said the bill “isn’t going anywhere” but acknowledged that anti-abortion Republicans will look for a way to get it on the agenda.

“Republicans have shown they’ll go to just about any length to limit access to care,” Murray said. “They’ve put politics between women and their health care. They’ve put employers between women and their health care. They’ve even threatened to shut down the government over this very issue. They’ve shown that this isn’t about what’s best for women, men, and their family planning decisions. Instead it’s about their political calculations. It’s about appeasing the far right. And it’s about their continued efforts to do whatever it takes to push their extreme agenda.”

There has been a flurry of activity in several state legislatures seeking to adopt laws working against Planned Parenthood of Southeastern Pennsylvania v Casey, a 1992 ruling by the U.S. Supreme Court which held that a woman has a right to an abortion until the fetus attains “viability,” a status that is generally reached at or about 28 weeks under the ruling.

The Texas legislature is considering a measure in special session that would permit the state to prohibit abortions after 20 weeks. An earlier attempt to move the line was thwarted by a filibuster. North Carolina is likewise engaged in debate over a 20-week limit.

If successful, Texas and North Carolina will be the tenth and eleventh states to impose a 20-week limit since 2010, joining a list that includes Nebraska, Alabama, Arizona, Georgia, Idaho, Indiana, Kansas, Louisiana and Oklahoma. North Dakota prohibits the procedure as soon as a heartbeat can be detected, or as early as six weeks. Arkansas has a 12-week limit. Idaho’s law was struck down by a federal judge who called it unconstitutional.

The issue of reduced time frames has not been addressed by the Supreme Court. It’s likely the high court eventually will be called on to render an opinion.

Establishing a 20-week limit carries some popular support but the split between supporters and opponents is fairly narrow according to recent polling. A United Technologies/National Journal Congressional Connection Poll conducted by Princeton Survey Research Associates International on June 20-23 showed that 48 percent of those questioned support the outlawing of abortions after 20 weeks except in cases of rape or incest while 44 percent opposed.

On abortion generally, a Gallup Poll conducted May 2-7 found that 26 percent of those questioned maintained that abortion should always be legal, 52 percent said it should be legal sometimes and 20 percent said it should always be illegal.

The abortion question dropped into the Senate’s lap on June 18 when the House voted 228-196 to ban the procedure after 20 weeks. The tally broke down mostly along partisan lines – six Democrats supported the measure while six Republicans voted against it. Rep. Trent Franks (R-Ariz.), the prime sponsor, said the 20-week limit was set because it represents the stage where a fetus can feel pain – a claim disputed by some medical experts.

House Speaker John Boehner (R-Ohio) called the legislation, titled the Pain-Capable Unborn Child Protection Act, “the most significant pro-life legislation to come before Congress since enactment of the ban on partial-birth abortions. We have a moral obligation to defend the defenseless, and we will continue to fight to ensure our nation’s laws respect the sanctity of unborn human life.”