WASHINGTON — Republican leaders hope House passage of bills targeting Planned Parenthood and curbing some abortion procedures will mollify fractious conservatives demanding a face-off with President Barack Obama that could trigger a federal shutdown.

The GOP-run chamber was on track to approve the two measures today, despite White House veto threats and opposition from most Democrats. One would block Planned Parenthood’s federal funds for a year. The other would inflict criminal penalties on doctors who don’t try saving infants born alive during abortions.

The bills were a reaction to videos showing Planned Parenthood officials casually describing how they provide researchers with tissue from aborted fetuses. The debate also underscored how the age-old fight over abortion could affect next year’s elections because it touches emotional hot spots among each side’s most loyal partisans and could be pivotal as each party tries wooing female voters.

“It’s about preserving a pipeline of funding to the nation’s largest abortion provider,” Rep. Martha Roby, R-Ala., said of Democrats arguing that Planned Parenthood provides irreplaceable health services for women. “We all get that. So let’s drop the phony women’s health charade.”

“This bill is spiteful, it’s mean-spirited and it is cruel,” Rep. Rosa DeLauro, D-Conn., said of the measure halting Planned Parenthood’s funds. “It tells millions of low-income Americans, ‘Forget your health, you can just die.’ “

The anti-abortion activists who secretly recorded the videos say they show that Planned Parenthood is illegally profiting from organ sales. The organization says it’s broken no laws and is being victimized by deceitfully edited recordings.

The White House, in a statement released Thursday evening, said Obama called the shutdown threat “a game of chicken with our economy that we cannot accept.”

It was unclear if House approval of the two bills would help House Speaker John Boehner solve a political Rubik’s Cube. The Ohio Republican’s twin goals: avoiding a shutdown fight that GOP leaders warn would set voters against the party, while simultaneously appeasing conservatives who might try to oust him for not adequately confronting Obama.

“Our leaders wave the white flag every time there’s a confrontation,” said Rep. Mark Salmon, R-Ariz. Rep. Thomas Massie, R-Ky., said Boehner wants to “implement what the lobbyists want, not what the constituents of our district want.”

At a closed meeting Thursday among House Republicans, leaders unveiled internal polling that attendees said showed most people would oppose a government shutdown — even those who have seen the videos and oppose financing Planned Parenthood.

Many Republicans argued that the polling showed a shutdown fight would be damaging and unwinnable, especially since Senate Democrats already derailed a bill erasing Planned Parenthood’s funds.