Chief Justice John G. Roberts Jr., who probably holds the crucial vote, indicated that he was inclined to strike down overall limits on contributions to several candidates, but perhaps not separate overall limits on contributions to several political committees.

At a news conference Tuesday afternoon, President Obama said the case had the potential to destroy what was left of campaign finance regulation.

“The latest case would go even further than Citizens United,” he said. “It would say anything goes: there are no rules in terms of how to finance campaigns.”

The case, McCutcheon v. Federal Election Commission, No. 12-536, is a sort of sequel to Citizens United, which struck down limits on independent campaign spending on television advertisements and the like by corporations and unions. The new case is an attack on the other main pillar of federal campaign finance regulation: limits on contributions made directly to political candidates and party committees.

The case was brought by Shaun McCutcheon, an Alabama businessman, and the Republican National Committee. It is in one way modest and in another ambitious. It does not attack the familiar basic limits on contributions from individuals to candidates or party committees. The $2,600 cap on contributions to a given candidate in each election, for instance, is not at issue in the case.