Last Updated Jul 28, 2015 4:34 PM EDT
The Senate will vote soon on an effort to block federal funding to Planned Parenthood, according to Sen. Majority Leader Mitch McConnell, R-Kentucky.
"[I]t's our plan to have a vote on proceeding to a measure that they support sometime before we break for the August recess," McConnell told reporters Tuesday.
The measure is not expected to get the 60 votes needed to move forward in the Senate. There are 54 Republicans and just a few anti-abortion Democrats, though some abortion-rights Democrats have avoided defending the comments that Planned Parenthood officials made in the videos.
Still, Sen. Rand Paul, R-Kentucky, said that win or lose, simply having the vote will be "a huge victory for conservatives" opposed to abortion. Planned Parenthood has been under fire since some of its officials have appeared in videos, secretly recorded by an anti-abortion group, discussing procedures for obtaining fetal tissue for research.
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Asked by lawmakers Tuesday about Planned Parenthood, Health and Human Services Secretary Sylvia Burwell said the dispute over how the group gets fetal organs for research involves "passion and emotion and belief on many sides of the issue, and I want to respect that."
Burwell also told the House Education and the Workforce Committee, "There are statutes that guide the use of fetal tissue that are in place and should be enforced."
It is illegal to sell fetal tissue for profit, but legal for a group providing it to recover the costs of the procedure.
Planned Parenthood has said it has done nothing illegal or improper. It receives more than $500 million annually in government aid, including some state funds. Federal funds cannot be used for abortions except for pregnancies involving rape, incest or where the mother's life is in danger.
Paul, who has been toward the bottom in public opinion polls on GOP presidential candidates, credited his "persistence" in achieving a Senate vote.
House Republicans say there are no plans for a vote in that chamber before it begins its recess, probably on Wednesday. The Senate is scheduled to leave the Capitol at the end of next week.
The Center for Medical Progress, the anti-abortion group, released its third video Tuesday, this one showing Planned Parenthood officials and a former technician for a private company that procures fetal tissue discussing their procedures.