– Millionaires and billionaires are increasing their influence in federal elections, leaving political parties to play more limited roles, and raising questions about who sets the agenda in campaigns.

In a handful of key Senate races, the biggest and loudest players so far are well-funded groups that don’t answer to any candidate or political party. That can make it hard for voters to know who is responsible for hard-hitting TV ads and other “messaging.”

Candidates and parties acknowledge the outside groups can be helpful. And last week’s Supreme Court decision voiding overall limits on contributions to candidates, PACs and political parties may give the parties a modest boost.

But some party officials say even friendly independent groups can be unpredictable, unaccountable and worrisome.

“The difficulty with outside groups is they may not understand what’s happening inside a district,” said Rep. Steve Israel of New York, who oversees Democrats’ House races this year. He said he sometimes sees TV ads from pro-Democratic groups “and I cringe. I don’t know where they’re going.”

Nicolle Wallace, a top aide in the 2004 and 2008 Republican presidential campaigns, echoed that view.

“When you land in a battleground state, and you plan a speech the next day on, say, military spending,” she said, it can be jarring to see a barrage of supposedly friendly TV ads on a different topic.

The clout of the Republican and Democratic parties, which have dominated U.S. politics since the Civil War, is now more in doubt than it was a few years ago.

“It obviously diminishes the roles of the parties because we have this large influx of outside money,” said Sen. John McCain of Arizona, the GOP’s 2008 presidential nominee. Massive spending with no accountability, he said, is a scandal waiting to happen.

The Supreme Court last week removed limits on the overall amount that wealthy donors can give to candidates and political parties.

But the court retained limits on how much a donor can give to any one campaign or party committee. More important, it didn’t touch the relatively new type of super PACs.

The court ruling may enable the political parties to raise more money in various ways. But the impact will be modest for each party’s three traditional committees, which focus on House races, Senate races and the overall party.

As the outside groups have gained muscle, the leaders of both national parties concede they’ve taken on more technical and mundane duties.

“I have to focus on the things that I most control,” said Reince Priebus, chairman of the Republican National Committee. Those include the mechanics and fixing data and digital problems.

Rep. Debbie Wasserman Schultz of Florida, chairman of the Democratic National Committee, said: “We’re a lot more tactical and granular these days than we were a few years ago.”