Washington (CNN) The fight over funding for Planned Parenthood shifts to a must-pass government funding measure this fall after a procedural vote in the Senate on legislation that would have barred all federal funds for the group failed on Monday.

The vote was 53-46, meaning the measure failed the get the 60 votes needed to overcome a Democratic filibuster on bringing the bill up for debate.

Planned Parenthood has come under intense scrutiny after an anti-abortion group released a series of videos it says shows that the nonprofit group is making money off of the sale of fetal tissue, a practice the group denies.

Conservatives in both the House and Senate are demanding that their leaders attach a provision to any spending bill to block additional federal funds from going to Planned Parenthood.

Texas Republican Sen. Ted Cruz told reporters to GOP should use "any and every procedural tool available" to defund Planned Parenthood. When pressed if that meant forcing a government shutdown over the issue Cruz, argued Democrats should be the ones asked if they supported "continued taxpayer funding for an organization that has been caught on film, apparently repeatedly admitting multiple felonies -- to buying and selling body parts."

Federal agencies run out of money at the end of September, and Congress is expected to take up some type of short-term spending bill next month.

Cecile Richard, president of Planned Parenthood Federation of America, called the failed GOP effort on the bill on Monday evidence that the issue was a "political non-starter."

"While some extreme Republicans may continue to insist on shutting down the government in order to deny health care, including birth control, to millions of women, that is a fight the American people have zero appetite for and a fight these extremists will not win," Richards said in a statement.

White House press secretary Josh Earnest, appearing on CNN's "New Day" on Monday, said that he has not viewed the videos. But he added, "what the President has said is that Planned Parenthood provides valuable services, health care services for men and women across the country. He would veto any legislation that tried to advance wholesale defunding for Planned Parenthood."

Republicans on Capitol Hill have clashed with President Barack Obama over federal money for Planned Parenthood before.

In 2011, House Republicans passed a spending bill that stripped money for Planned Parenthood, and the fight over the issue came close to causing a government shutdown. Right before the deadline, House Speaker John Boehner negotiated a compromise that didn't include a defunding provision.

JUST WATCHED Rand Paul vows to defund Planned Parenthood Replay More Videos ... MUST WATCH Rand Paul vows to defund Planned Parenthood 03:54

GOP Sen. Rand Paul, who pressed Senate leaders for the vote on Planned Parenthood this week, was reluctant to draw a line in the sand.

"I support any legislation that will defund Planned Parenthood. But (I) don't think you start out with your objective to shut down government," the Kentucky senator told CNN's Jake Tapper on Sunday.

Iowa Sen. Joni Ernst, the sponsor of the GOP bill that failed to advance on Monday night told reporters, "These videos are not going away."

But when asked if she would vote for a government funding bill that was linked to defunding Planned Parenthood, she said she wasn't at that point yet, and wasn't "going to discuss that."

Senate Majority Leader Mitch McConnell, also a Kentucky Republican, declined to rule out attaching a provision to the spending bill in September.

"We're going to discuss how to fund the government after the recess," he told reporters last week.

Boehner has emphasized that multiple congressional committees are launching investigations into the videos and said he is awaiting more facts before deciding any next steps.