It also has dimmed hopes for broader efforts this year to start taming the costly and fast-growing "entitlement" programs of Medicare and Social Security.
The result is a new round of deficit reduction that tilts more toward Republicans' wishes than many people would have expected after Obama won re-election with a campaign that called for higher taxes on the rich.
Democrats thought House Republicans would accept some new revenues last month to minimize military cuts and to pressure liberals to confront entitlement spending. Instead, Republicans seem more determined than ever to block tax increases on high incomes, whatever the political risk.
It's now the overriding priority for GOP lawmakers -- even if they hold a different view of payroll taxes on wage earners. With relatively little debate, Republicans and Democrats this year raised the payroll tax rate, which funds Social Security, after granting a two-year reduction.
In all, two years of budget debates have yielded laws to reduce deficits by nearly $4 trillion over 10 years, a point of pride for Republicans. About $620 billion of that will come from tax hikes made inevitable by the "fiscal cliff" legislation, resolved on Jan. 1. The rest will come from spending cuts and savings on interest.
The ratio disappoints liberals. They recall that Congress' top Republican suggested $800 billion in new revenue, and Obama proposed $1.2 trillion or more, in "grand bargain" talks that started in 2011 but never reached fruition.
"Somehow we ended up with $600 billion," and with no provisions to rein in entitlements, says Jim Kessler of the Democratic think tank Third Way. "It was an enormous missed opportunity."
For House Republicans, the no-income-tax-increase stand is more doctrine than strategy. Whether lucky or strategic, however, they feel they outfoxed Obama on deficit-reduction policies this time.
When a new "fiscal cliff" law was about to raise income tax rates on nearly all U.S earners in January, GOP leaders accepted Obama's offer to limit the increase to incomes above $450,000. It was a concession by the president, who had campaigned for a somewhat broader tax hike.
Republicans never reciprocated, however. That cleared the way last week for across-the-board "sequester" spending cuts, once considered too damaging to enact. The deal contains none of the new revenues that Democrats had hoped would follow their compromise on the fiscal cliff.
"It a result of botched negotiations on the fiscal cliff," Kessler said. "There is now no forcing mechanism for Democrats to come to the table on entitlements and for Republicans to come to the table on revenue."
The government is cutting into discretionary spending rather than investing in education, infrastructure and other future-oriented priorities, Kessler said.
Republicans say income tax rate hikes inhibit hiring. Democrats note that the federal tax burden, as a portion of the economy, is the lowest it has been since 1950. Also, nonpartisan studies show that the Bush-era tax cuts contributed heavily to the deficit.
Some Republicans say they outflanked Obama last week simply by adamantly opposing higher income taxes. It's a priority they reinforced at a January gathering in Williamsburg, Va.
"The strategy we've been embarked on since Williamsburg -- which is no budget, no pay; lock in the sequester savings; get the CR done -- so far, that's working," said Rep. Jim Jordan of Ohio, a prominent House conservative. He was alluding to House efforts to force senators to pass a budget (or forgo their pay), and to open the way for a "continuing resolution" to keep the government operating beyond March 27, with no increase in revenues.
Kevin Smith, a spokesman for House Speaker John Boehner, said: "We're exactly where we set out to be a few weeks ago."
The GOP strategy carries risks. Polls show Americans are more inclined to blame Republicans than Democrats if the budget reductions damage the economy or significantly inconvenience people's day-to-day lives.
Louisiana Gov. Bobby Jindal and other non-Washington Republicans say congressional Republicans are too obsessed with austerity and budget numbers, risking a public backlash if programs are cut too deeply or unwisely.
A CBS News poll finds large majorities of Americans saying they want both parties to compromise rather than hold fast to their positions. Self-identified Democrats, however, embrace compromise more than Republicans do.
GOP strategist Mike McKenna thinks House Republicans took a smart, calculated risk by letting the sequester cuts take place. "Most people don't interact with the federal government a lot," he said.
While most Americans support a mix of budget cuts and tax increases to reduce the deficit, McKenna said, they realize the payroll tax rose in January, along with the tax on incomes above $450,000.
With the deficit-spending battles apparently cooling for a while, Congress can focus more heavily on immigration, gun control and other issues.
Congressional Republicans say they're confident that few if any changes will be made to gun laws. As for immigration, most are taking a wait-and-see approach.
Many conservative activists oppose "amnesty" for illegal immigrants. But Republican strategists say the party will struggle to win presidential elections unless it improves its relationship with Hispanic voters, many of whom see immigration as important symbolically and substantively.
House Republicans "are so caught up in the sequester thing, they're not thinking four weeks down the road," McKenna said.
For now, they seem content without a grand strategy, and some Democrats are wincing.
Democratic consultant Jim Manley, who confers often with Obama aides, said those aides feel the president used his fiscal cliff leverage to his advantage on Jan. 1. But on the sequester, they concede that Republicans returned the favor and had the upper hand, Manley said.
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