Washington CNN  — 

Under pressure from House conservatives, House Speaker John Boehner and other Republican leaders have scheduled a vote for Thursday night on a measure that would block a controversial abortion law passed by the Washington city council.

The law, approved in December, would ban city employers from taking punitive action against employees for using abortion services or birth control. Under the Constitution, Congress has the authority to nullify measures passed by the Washington city council.

But time is running out, because both the House and Senate need to pass a resolution of disapproval 30 days after the measure was transmitted to Capitol Hill. The House Oversight committee approved a resolution of disapproval last week, but the deadline for full congressional action on the bill is Friday. The House vote is expected around 10 p.m. Thursday and is expected to pass, mostly along party lines.

“We got a variety of members to push really hard on leadership to do the right thing,” Texas Rep. Bill Flores, who heads the conservative Republican Study Committee, told reporters after learning their efforts prevailed to get a vote on the abortion measure.

The House Oversight committee measure also passed on a party-line vote, but supporters grew frustrated when they weren’t able to get leaders to lock in a full House vote. At a closed-door meeting of House Republicans on Wednesday, a group pressed leaders to bring up the resolution this week.

Rep. Tim Huelskamp, R-Kansas, told CNN he argued that social conservatives are “still upset and distrustful of our party” after House Republican leaders pulled a bill that banned later-term abortions from the floor earlier this year.

“Initially they said no,” Huelskamp said about moving forward with the resolution on the D.C. law. But Huelskamp, a frequent critic of Boehner and other party leaders, said he was glad some House Republicans had changed their positions, adding that leaders were nearing an agreement on a revised version of the late-term abortion legislation.

Flores and other RSC members planned to take their case to the House floor later Wednesday to publicly complain that their own leadership was ignoring the issue, according to an aide familiar with the discussions. But after talking with leaders, Flores declined to “get into the weeds” on the internal Republican talks and said he was pleased leaders agreed to the vote.

Another group of conservatives, the House Freedom Caucus, also pushed for a vote, and in a statement, said the law “would discriminate against D.C. residents with pro-life views.” Proponents of the Republican resolution also maintain that anti-abortion rights groups in Washington would be faced with decisions about hiring candidates that could conflict with their religious beliefs.

House Democrats say the resolution was a political move to appeal to religious conservatives and is actually counter to Republican efforts to shift controversial issues away from the federal level.

“So much for people who talk about states’ rights and local control,” Democratic Caucus Chairman Xavier Becerra said after hearing about the vote.

Democrats say the Republican bill is another effort to intrude into employees’ personal decisions about health care, and warned it could cause workers in D.C. who elect to use abortion services to be fired.

“What a statement to women across America – that a mostly older male body is telling women what they can do with their bodies,” Becerra told CNN.

But even Flores admitted the House vote is as far as the issue will go, and Congress won’t be able to block the D.C. law. To make matters worse for the bill’s prospects, the White House threatened to veto the House measure on Thursday.

“The House will make the deadline. Of course, the Senate probably won’t, and the President wouldn’t sign it,” Flores said. “But at least the American people will know where the House of Representatives stands on pushing back on the attempts of the D.C. city council to inhibit religious liberty.”