Democrats, including Minnesota Sens. Amy Klobuchar and Al Franken, started their campaign-season push Monday for a constitutional amendment aimed at curbing special interests' financial clout in elections, an effort the party hopes will appeal to voters come Election Day.

The amendment would allow Congress and states to limit the money raised and spent in election campaigns, curbs that have been weakened by Supreme Court decisions in recent years.

Though it passed a procedural hurdle in the Senate on Monday, the measure has little of chance of passing the upper chamber, and leaders in the Republican-controlled U.S. House have no plans to vote on it.

Democrats around the country have spent months criticizing the billionaire Koch brothers, who have contributed large sums to conservative groups that are spending millions to try defeating Democratic senators.

Many lawmakers have also used the threat of the duo's donations as a tool to raise campaign cash: at least two Franken fundraising emails in the past week have mentioned the Koch brothers.

Franken and Klobuchar joined a press conference Monday on Capitol Hill where Democrats touted the amendment.

Republicans say limiting campaign spending by outside groups would violate free speech and have accused Democrats of pushing the measure to score political points.

Outside groups have spent $189 million on congressional campaigns since January 2013, according to the nonpartisan Center for Responsive Politics, which monitors political spending. That's more than triple the $57 million spent to this point in the 2010 campaign — which, like this year, featured only congressional races and not a presidential contest.

The proposed amendment authored by Democratic Sen. Tom Udall of New Mexico, and co-sponsored by Franken and Klobuchar, would let lawmakers roll back a 1967 Supreme Court decision which found that limiting campaign spending by outside groups would violate their free speech.

The legislation would also let Congress address the 2010 Citizens United case, which allowed unfettered independent spending by corporations and unions, and last April's ruling that lets individuals contribute to as many candidates as they'd like.

The Associated Press contributed to this report.