Social conservative leaders are lashing out at House Republicans after they abandoned a bill banning abortions after the 20th week of pregnancy. 

The backlash underscores the internal pressure on party leaders, who already are facing criticism from the GOP's right flank over their handling of immigration and other issues. 

"I am disgusted by this act of moral cowardice," Russell Moore, president of the Southern Baptist Convention's Ethics & Religious Liberty Commission, said in a statement. "If the House Republicans cannot pass something as basic as restricting the abortion of five-month, pain-capable unborn children, what can they get done?" 

Republicans originally had teed up the "Pain Capable Unborn Child Protection Act" for a vote on Thursday to help mark the anniversary of the landmark Supreme Court Roe v. Wade abortion decision. It also would coincide with the annual March for Life rally in Washington. 

But a handful in the Republican conference, including Reps. Renee Ellmers, R-N.C., and Jackie Walorski, R-Ind., pulled their support citing concerns about the language for the bill's exemptions. 

Most notably, one provision would exempt victims of rape -- but only those who reported incidents to law enforcement. According to statistics from the Department of Justice, only one-third of rape victims report it. 

Without the support of the entire conference, GOP leaders pulled the bill and swapped it out with another measure banning federal funding for abortions -- a measure already in effect and which Congress usually renews. It's almost identical to the bill the House passed last January. 

The "Pain Capable Unborn Child Protection Act" wasn't expected to become law. President Obama threatened to veto the measure if it ever hit his desk. 

But the inability of House Republicans to pass it is raising new questions about the future of social issue legislation in the 114th Congress, despite Republicans' expanded majority. 

Family Research Council President Tony Perkins, in a written statement, applauded GOP leadership for "remaining committed to advancing pro-life legislation." 

But he said his group is "disappointed" by the developments on Thursday. 

"The excruciating pain that unborn babies feel at five months is a matter of biology, not a matter of belief. It is time that Congress put an end to this barbaric horror," he said. 

Capitol Attitude is a weekly column written by members of the Fox News Capitol Hill team. Their articles take you inside the halls of Congress, and cover the spectrum of policy issues being introduced, debated and voted on there.