‘‘What are the races that are going to determine a pro-business majority’’ in Congress, Engstrom said of how the group decides where to spend.

Besides opening the door for unlimited spending by large organizations, the Citizens United ruling also led to the formation of obscure groups that pump money into House races with voters knowing little about who is behind the money.

The Treasure Coast Jobs Coalition, formed this July, has spent $2.2 million opposing Democrat Patrick Murphy’s attempt to unseat GOP Rep. Allen West of Florida. Much of its money comes from casino magnate Sheldon Adelson and New Jersey pharmaceutical executive Richard Roberts. Both often contribute to GOP causes.

Murphy’s campaign has been helped by about $170,000 in spending by American Sunrise, a political committee started in January and financed largely by Murphy’s father, Thomas.

In a battle for an open House seat in northwestern Connecticut, the Government Integrity Fund is spending $1.1 million on ads attacking Democrat Elizabeth Esty, a former state legislator, saying, ‘‘Keep tax and spend politician Elizabeth Esty out of Congress.’’

The website of the Integrity fund, based in Ohio, says it favors individual freedom and limited government. Federal election reports reveal little about its contributors, and listed officials did not return messages seeking more information about why they entered the Connecticut contest.

Chris Cooper, spokesman for Esty’s Republican opponent, Andrew Roraback, complained that Democratic ads unfairly link Roraback to tea party politicians. ‘‘If these outside dollars can help tell the truth about Andrew’s record, then we feel it will even the playing field,’’ Cooper said.

He noted that Esty has received nearly $1.1 million from the Democratic Congressional Campaign Committee.

Democrats argue there is a difference between the Government Integrity Fund’s undisclosed donors and their party’s congressional campaign fund, whose donors are reported publicly.

‘‘It has a huge impact,’’ Rep. Steve Israel, D-N.Y., who heads the Democratic committee, said of the Integrity Fund’s spending. ‘‘It’s a hijacking of democracy.’’

In the northern Chicago suburbs, freshman GOP Rep. Joe Walsh has struggled against his well-financed Democratic opponent, Tammy Duckworth, a wounded Iraq war veteran and a former official with the Department of Veterans Affairs. In recent weeks, the Now or Never PAC, a Missouri-based political action committee, has spent $1.8 million to help Walsh.

The bulk of the group’s money has come from the conservative Americans for Limited Government, based in Virginia, which Walsh’s congressional website says he helped found.

Walsh spokesman Justin Roth said the lawmaker has had no contact with that group for over a decade and knew nothing of its contribution to Now or Never.

Officials from Limited Government and Now or Never said Walsh had nothing to do with Now or Never’s decision to assist him.