Some Republicans, however, fear taxpayers' money is at least indirectly used for abortions, despite federal law that prohibits such use of taxpayer funds.
"Planned Parenthood is a private non-profit organization that should be sustaining itself, and their corporate business model relies on abortions," said New Hampshire Republican Sen. Kelly Ayotte in an interview posted on the Susan B. Anthony List website.
"Abortion yields 37 percent of all Planned Parenthood revenues by conservative estimates," she said. "I don't think it's appropriate to provide taxpayer dollars."
Three Senate Republicans -- Susan Collins of Maine, Scott Brown of Massachusetts and Lisa Murkowski of Alaska -- have publicly opposed defunding Planned Parenthood, saying the move goes too far.
And 41 senators -- all 39 Democrats and independent Sens. Bernie Sanders and Joe Lieberman -- have vowed they'll filibuster any bill that includes such a cut.
"The dangerous, ideological cuts that passed through the House are never, never, never going to pass the Senate," Sen. Chuck Schumer, D-N.Y., told a cheering crowd of Planned Parenthood supporters at a rally outside the capitol.
But many Republicans may be willing to take a stand on the Planned Parenthood rider or any number of other controversial measures, eager to appeal to their conservative base while also achieving greater budget savings.
"Our goal is real clear: We're going to fight for the largest spending cuts we can get, and the policy riders that were attached to them, because we believe that cutting spending will lead to a better environment for job creation," House Speaker John Boehner said Wednesday.