WASHINGTON — In its first major campaign finance case since the Citizens United ruling in 2010, the Supreme Court is considering whether to undo some limits on contributions from the biggest individual givers to political campaigns.

The justices will hear arguments Tuesday, the second day of their new term, in a dispute between the Obama administration and Republicans who are challenging the contribution limits as a violation of First Amendment rights.

Supporters of campaign finance laws say the case poses a threat to the contribution limits that Congress first enacted in 1974, in the wake of Watergate abuses.

In 2010, the 5-4 ruling in Citizens United freed corporations and labor unions to spend as much as they wish on campaign advocacy, as long as it is independent of candidates and their campaigns. That decision did not affect contribution limits to individual candidates, political parties and political action committees.

Now, Republican activist Shaun McCutcheon of Hoover, Ala., the national Republican party and Senate Republican leader Mitch McConnell of Kentucky want the court to overturn the overall limits on what contributors may give in a two-year federal election cycle.

The total is $123,200, including a separate $48,600 cap on contributions to candidates, for 2013 and 2014.

The partisan-tinged campaign finance case comes to the court amid a tense stalemate over the federal budget that has shuttered parts of the government, but so far has not affected the Supreme Court.

Chief Justice John Roberts formally opened the new term Monday without any reference to the shutdown.

The court has announced it will operate normally at least through the end of this week.