While Republicans traditionally support free-trade deals, for example, many Tea Party candidates oppose them. Establishment Republicans have held on-and-off negotiations with the White House for an energy bill that would promote alternative energy sources, among other things, but almost all of the Tea Party candidates question the science behind the idea of global climate change.
Tea Party candidates say they are determined not to be co-opted by Washington, even if that means battles with fellow Republicans.
"Republicans are every bit as much to blame as Democrats for the mess we're in," Senate nominee Ken Buck of Colorado said in an interview this summer. "We are so sick of the establishment. It's not the Democrats who are the enemy. It's the Republicans who go back and spend more because they want to get re-elected; they want to bring goodies back to their state."
Former congressman Dick Armey, who became majority leader when Republicans won the House in 1994, says the Tea Party has the upper hand.
"The Tea Party activists are transforming the Republican Party," Armey, who now heads a Tea Party-aligned group called FreedomWorks, said in an interview. "The establishment types that are too 'sophisticated' for this work, let them cast their votes. They are well aware of the fact this grass-roots movement is out there.
"It's alive; it's well, and it's going to be active in the next election."
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No issue has ignited Tea Party passions more than a conviction that federal spending is out of control.
Many Americans agree. Asked in a USA TODAY/Gallup Poll to name the most important problem facing the nation today, the federal budget deficit and public debt ranked among the top five issues.
Actually reining in the deficit is going to be harder than talking about it, though. Republicans who have pledged to cut the budget by $100 billion haven't specified exactly how.
"The next two years are going to be about the politics of subtraction," Pitney says. Shrinking the government in any meaningful way is likely to mean raising taxes, curtailing Medicare and Social Security benefits and taking other painful steps.
A bipartisan commission is due to report Dec. 1 on recommendations to curb the deficit, though it's not clear whether even the 18-member panel will be able to command the 14 votes it needs to send a plan to Congress for a vote.
And in Congress, both sides may be less open to compromise than before. Six of the 54 moderate "Blue Dog" Democrats who have pushed fiscal discipline are leaving the House; most of those who are running are in competitive contests. Losses in their ranks would leave a more liberal Democratic caucus that would be deeply resistant to cuts in social programs.
On the Republican side, too, opposition to tax hikes is likely to be intensified by the Tea Party.
"The people gone are the middle ones, the centrists in both parties," says political scientist Larry Sabato of the University of Virginia. With the ranks of moderates thinned, "I don't think they could agree on the wording of a Mother's Day resolution."
The first fiscal tests loom in the lame-duck session of Congress just after the election. On the table: Spending bills to fund the government and extension of the Bush-era tax cuts.
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White House officials say it may be possible to reach bipartisan agreement on a few major pieces of legislation — for instance, to renew the No Child Left Behind law, which ties federal funds to accountability standards for school districts.
By and large, though, without muscular Democratic majorities in Congress Obama will have to turn from negotiating grand deals on Capitol Hill to taking smaller steps on policy by issuing executive orders and regulations.