WASHINGTON — The Supreme Court is opening for business in the midst of a partial government shutdown.

The justices take the bench today for the start of their new term with important cases about campaign contributions, housing discrimination, government-sanctioned prayer and the president’s recess appointments already on tap. Abortion, contraceptive coverage under the new health care law and cell phone privacy also may find their way onto the court’s calendar.

The court announced it will operate normally at least through the end of this week. The justices are hearing six arguments, including a challenge to limits on campaign contributions.

The new term may be short on the sort of high-profile battles over health care and gay marriage that marked the past two years. But several cases ask the court to overrule prior decisions — bold action in an institution that relies on the power of precedent.

“There are an unusual number of cases going right to hot-button cultural issues and aggressive briefing on the conservative side asking precedents to be overruled,” said Georgetown University law professor Pamela Harris, who served in President Barack Obama’s Justice Department.

Paul Clement, a frequent advocate before the court and the top Supreme Court lawyer under President George W. Bush, agreed the opportunity exists for dramatic precedent-busting decisions. But Clement said each case also offers the court “an off-ramp,” a narrower outcome that may be more in keeping with Chief Justice John Roberts’ stated desire for incremental decision-making.