Under the Affordable Care Act, employers are required to cover the cost of contraception with insurance.
Religious groups argue that they should be exempt from the requirement because it violates religious liberty.
A tie would uphold lower court rulings in support of the administration but not set a national precedent.
The court now has eight justices after conservative Justice Antonin Scalia died in February.
Senate Republicans are blocking efforts by President Barack Obama to fill the vacancy, making split decisions more likely.
The Obama administration has already agreed to a compromise for non-profit groups with religious ties that allows them to avoid directly providing birth control in health plans for employees.
Opposing groups argue this is not enough and do not want any link to providing contraception.
The groups view some forms of contraception as equivalent to abortion.
The Little Sisters of the Poor, a charity that cares for the elderly, and other Roman Catholic groups were among plaintiffs.
In oral arguments on Wednesday, Justice Anthony Kennedy, who usually is the deciding vote in divisive cases, expressed doubts about the government's case.
Justice Kennedy's questions signalled that he would join with the three conservative justices in favouring the Christian groups.
"They think that complicity is sinful," Chief Justice John Roberts said of plaintiffs.
The four justices who make up the court's left wing appeared to side with the Obama administration.
Justice Elena Kagan said the religious groups "were objecting to objecting."
For 90 minutes, the court heard arguments on whether non-profit groups opposed to the contraception requirement can use a 1993 law, the federal Religious Freedom Restoration Act, to object to the administration's compromise.
The hashtag #HandsOffMyBC was trending in Washington on Wednesday, mostly being tweeted by those who side with the Affordable Care Act requirement.
Democratic presidential candidate Bernie Sanders used the hashtag, tweeting: "No matter where you work or what you do, your birth control decisions should be up to you."
House of Representatives Speaker Paul Ryan tweeted his support for the religious groups, saying that "We should do everything we can to let people live out their faith".
A final ruling, if reached, will be announced in June.
The US Supreme Court appeared to be evenly divided over a case about faith-based groups indirectly providing contraception in employee health plans.