Even if they manage to overcome the political obstacles — big ones like a Democratic filibuster, a presidential veto, or a battle royal over shutting down the government — they may still collide with Medicaid law. The fight could leap from Congress to the courts.

The Senate has planned a test vote Monday on a bill to halt federal funding for Planned Parenthood after four sensational undercover videos by a previously unknown anti-abortion group portrayed the organization as allegedly profiteering from illegal fetal tissue sales — a charge Planned Parenthood denies.

Planned Parenthood got most of its $528 million in taxpayer support last fiscal year from two main pots of money — the Medicaid health care program for low-income people and grants such as the Title X family planning program.

By law, federal dollars don’t pay for abortions except in limited circumstances involving rape, incest or protecting the life of the woman.

If any bill to cut funding to Planned Parenthood became law, stopping the flow of Title X money would be relatively easy. Congress controls that money and can decide who gets how much, or who gets none at all. Even there, the money goes out in grants to states and organizations over a multiyear cycle, so a cutoff might not be simple or immediate.

But severing Planned Parenthood from Medicaid could be a lot more complicated, and that’s the bigger chunk of change. Planned Parenthood says roughly 75 percent of its government funding is state and federal Medicaid dollars, though it wouldn’t give a breakdown.

When states have tried to expel Planned Parenthood clinics from their Medicaid programs, they’ve ended up in court. The same thing could happen to a federal law.

Attorneys interviewed said Medicaid law has long protected a patient’s right to flexibility in choosing a health care provider (as long as the doctor, clinic or other provider accepts Medicaid). Those safeguards are particularly strong for access to family planning services, said Cindy Mann, an attorney with Manatt, Phelps & Phillips who until recently ran Medicaid for the Obama administration.

“That’s been an important provision to ensure access and allow women to make their own decisions about who to go to,” Mann said.

Planned Parenthood foes say they are confident that any defunding bill would take precedence. This new law, if enacted, would squeeze out prior statutes, said Douglas Johnson, legislative director of the National Right to Life Committee.

“The courts would have to go first to this statute,” Johnson said. “The later enactment always prevails.”

But that isn’t borne out by what’s happened at the state level. Ten states have cut family planning funds, according to the Guttmacher Institute. They include Arizona, Arkansas, Colorado, Indiana, Kansas, Michigan, North Carolina, Ohio, Oklahoma, Texas and Wisconsin.

Yet when several states tried to pull Medicaid funding from Planned Parenthood clinics, courts sided with Planned Parenthood and its backers, and stopped all or part of defunding bids in Tennessee, Indiana, Arizona and North Carolina.

Texas, under then-Gov. Rick Perry, did significantly cut family planning funds for clinics in 2011 as part of a larger crackdown on abortion providers. But the Obama administration said the move violated Medicaid requirements for offering a choice of family planning providers, and federal officials pulled Medicaid funding from the state for those services.

“The cases where states have tried to take away Medicaid funding from Planned Parenthood have all failed in one way or another,” said Susan Fogel, director of reproductive health for the National Health Law Program.

Providers can be barred from participating in Medicaid in some situations, Fogel said. They could be disqualified if they commit fraud or violate licensing laws or the Medicaid statute. The sting videos released by the Center for Medical Progress depict alleged wrongdoing, but Planned Parenthood hasn’t been formally charged with illegal activity or proved to have broken the law.

If Congress bars a qualified clinic from participating in Medicaid by pulling its funding, Fogel said it’s likely to be considered discriminatory against the clinics.

“Shutting down family planning clinics because of taking away money from Planned Parenthood only hurts the individuals who need those services,” Fogel said. “I’m sure that there would be immediate litigation to stop it in the courts.”

Abortion may make Planned Parenthood a lightning rod but the organization says abortion services make up only 3 percent of the health care it provides, according to its latest annual report. But the NRLC’s Johnson and other Planned Parenthood opponents are skeptical of that claim.

“This is the abortion mega-marketer of the country that we’re talking about,” Johnson said.

The clinics do provide preventive health services, such as breast and cervical cancer screenings, as well as testing and treatment for sexually transmitted diseases. Planned Parenthood Action Fund Executive Vice President Dawn Laguens said GOP-led efforts to defund its clinics would “block millions from getting basic health care” and it’s unrealistic to suggest other health providers could absorb that work.

Not so, say the bill’s sponsors. The legislation spearheaded by Sen. Joni Ernst (R-Iowa) would take the money no longer available to Planned Parenthood and give it to other health care facilities to provide women’s health care services.

“They would be able to go to one of the other community health centers,” Oklahoma Sen. James Lankford said. “In my state, there are four Planned Parenthood clinics and there are 60 community health centers.”

Jennifer Haberkorn contributed to this report.