Republicans don't seek to grind government to a halt. But they do aim to shrink its size by an amount currently beyond their institutional power in Washington, or popular support in the United States, to achieve. Democrats don't seek to cripple the United States with debt. But they do aim to preserve existing government programmes without the ability, so far, to set levels of taxation commensurate with their cost.
At bottom, it is the oldest philosophic battle of the American party system - pitting Democrats' desire to use government to cushion market outcomes and equalise opportunity against Republicans' desire to limit government and maximise individual liberty. And they are fighting it within a 21st-century political infrastructure that impedes compromise.
Those government initiatives include Social Security from 1930s Democratic president Franklin D Roosevelt's New Deal; Medicare and Medicaid from 1960s Democratic president Lyndon B Johnson's Great Society; and the 2010 national health care law, passed by the current president in his previous term. President Obama wants to keep them in roughly their current forms - even as the wave of baby boom retirements makes them costlier than ever.
His Republican opponents are the philosophic heirs of conservatives who opposed their creation in the first place. Beginning in 2009, they gained fresh momentum in the quest to roll them back. While the Great Recession depressed tax revenues, the Wall Street bailout and stimulus bill gave Americans sticker shock; deficits topped $1 trillion annually. So in 2011, the newly elected Republican House began pushing President Obama backward in budget fights that forced significant slowing of federal spending and some significant spending cuts.
Their climactic showdown over the debt limit in 2011 damaged the nation's credit rating. With both sides battered and exhausted, Republicans joined Democrats in seizing the so-called sequester as the means to end the impasse. Then Mr Obama stopped backing up - and moved to generate momentum of his own.
The right's soft spot, as Ronald Reagan and Newt Gingrich learned amid the conservative ascendancy of the 1980s and early 1990s, is the popularity of expensive "entitlements" serving the elderly. "Cut spending," as a general invocation, is popular. "Cut spending for your mother's Medicare" is not.
Mr Obama used his re-election campaign to isolate and attack that vulnerability. Acknowledging the need for some entitlement cuts, he offered voters this budgetary choice: his smaller cuts combined with tax increases on affluent Americans, or the Republicans' bigger ones without tax increases. More Americans, as polls have repeatedly shown, prefer Mr Obama's approach. He won the election.
Now the president is trying to wield his public opinion advantage as a club to back Republicans down. The budget cuts of 2011, like sequestration now, targeted smaller "discretionary" programmes that don't command the support Medicare and Social Security do. Mr Obama argues, and some Republicans agree, that Washington has cut most of what it can from those.
He continues to advocate comparatively modest Medicare cuts focused on reimbursements to doctors and hospitals - more near-term cuts, in fact, than Republicans have been willing to specify. But at one high-profile event after another, in Washington and across the country, he accuses Republicans of preferring reduced benefits for old and vulnerable Americans over higher taxes on the affluent.
Opponents blast him for "campaigning" instead of governing. Yet those events have become his method of seeking outcomes that negotiations with Republican leaders haven't produced. It worked soon after the election when he forced Republicans to accept some tax increases in the "fiscal cliff" deal. It worked again when Republicans declined to fight anew over the debt limit until May, at the earliest.
That doesn't mean it will work again by making Republicans accept a second tax increase. Over the last generation, polarisation has melted away the alloy that once narrowed differences between Republicans and Democrats, leaving both as masses of near-pure ideological ore. Note, however, that the Republican rank-and-file is purer - more conservative than the Democratic rank-and-file is liberal.
Resisting tax increases is a matter of such deep conviction that some senior Republicans believe House colleagues would fire John A Boehner as House speaker for conceding to Mr Obama again. For less ideological Republicans, the partisan composition of their districts and states can make following national opinion riskier (against a more conservative primary challenger) than defying it (against a Democratic general-election foe).
The difficulty of winning a second tax increase may ultimately make the president regret the fiscal-cliff deal, which brought only half the new revenue he considers necessary. For now, he seeks to grind down his opposition as the impact of sequestration mounts for air travellers, education programmes and the Pentagon. Against Republicans' solid edge on the issue of spending restraint (in this week's NBC News-Wall Street Journal poll), he wields wide Democratic advantages on helping the middle class and protecting Medicare, and a narrow one on handling taxes. The survey showed 50 per cent of Americans approve of Mr Obama's job performance. Only 29 per cent expressed a positive view of the Republican Party.
Among demographic groups, the only one viewing Mr Boehner's party more positively than negatively was white Southerners (by just 39 per cent to 35 per cent at that). More than twice as many Americans credited Mr Obama, as compared with Republicans, with emphasising themes of bipartisan unity.
Even if numbers like those don't threaten the House Republican majority in 2014, they alarm party strategists who've watched their nominees lose the popular vote in five of the past six presidential elections. Mr Obama's hope: the fact that Congressional Republicans are insulated from national opinion doesn't make them impervious to it.
©2013 The New York Times News Service