After Tuesday’s election results, victorious Republicans and chastened Democrats all claimed they would work for the American people. Maybe the sense of frustration and anger expressed by voters motivated the mostly nonpartisan sound bites heard Tuesday night and Wednesday.

But if Republicans and Democrats really wanted to demonstrate they were working for the people who elected them, they would visibly move away from their traditional corporate constituencies, meaning the groups that supply them with campaign money and political support.

There is a sense across much of America that the political elite in Washington are out of touch, and mostly work to advance the causes of their campaign financiers at the expense of average Americans.

Demonstrating that they were working for the American people and not those who finance much of their election efforts would mean the parties would have to rile their traditional supporters.

In the case of Republicans, that might mean closing tax code loopholes bought and paid for by corporate donations and intense lobbying. It might mean agreeing to a tax on the superwealthy, by adding one or two tax rates for those earning $1 million or maybe $10 million a year. And even if this money does not make a significant dent in the federal deficit, it would suggest that the ultra-rich were paying more of their fair share.

For Democrats, a similarly effective effort that would upset the base might mean pushing for an end to unsustainable public employee pensions and benefits. It would mean supporting education reform efforts such as merit pay and school choice that are opposed by teachers unions, traditional supporters of Democratic candidates.

Janet Daley, a columnist for the Telegraph newspaper in England, wrote that the tea party movement is partially fueled by a “rejection of what many Americans see as a conspiracy of the governing elite against ordinary working people.”

Daley went on to say that Americans view most politicians in Washington as “smug out-of-touch professionals.”

Going against the groups that traditionally support them and spent hundreds of millions of dollars helping them get elected would be a good way for Tuesday’s winners to prove that they get the message and they will work for average Americans.

President Barack Obama deserves credit in this area for his support of education reform, including teacher evaluations, merit pay and charter schools. Traditionally, Democrats and teachers unions reject teacher accountability, merit pay and school choice. Obama, and Education Secretary Arne Duncan, deserve credit for risking political consequences by pushing their education-reform agenda even if it annoys many teachers and all union officials.

Democratic members of Congress should join Obama in this effort. They should say that they understand that public sector employees, another big Democratic constituency, have pushed salary, benefit and pension packages to unsustainable levels. Democrats will demonstrate that they are working for average Americans when they push for changes to public employee benefits to minimize the damage to overburdened taxpayers.

On the Republican side, closing tax loopholes would help make the tax code more fair and ensure that more companies pay their fair share, rather than take advantage of targeted tax breaks. Some CEOs might squawk, but by taking such actions, Republicans would signal to Americans that they are working on behalf of the average worker and not the corporate lobbyist or check-writing executive. Both parties should push for more Wall Street reforms by enacting something similar to Great Britain’s special tax on multimillion-dollar in-vestment bankers’ bonuses and bringing back the Glass-Steagall Act, which separated risky investment banking from traditional commercial banking.

Leaders in Congress talk about doing what “the people” want. Challenging their political and financial patrons, demonstrating independence, is what the people want to see if they are to have faith that politics today is not a stacked deck.

Will it happen? Probably not. But if it did, it would be change we could believe in.