After they took power in January, the hard-line Republicans who dominate the House reached for a radical overhaul of American government, hoping to unravel the social safety net, cut taxes further for the wealthy and strip away regulation of business. Fortunately, thanks to defensive tactics by Democrats, they failed to achieve most of their agenda.

But they still did significant damage in 2011 to many of the most important functions of government, and particularly to investments in education, training and transportation that the country will need for a sound economic recovery.

With a threatened government shutdown in April, the Republicans pushed through spending cuts of about $25 billion over a decade. Then, in August, the agreement to raise the debt ceiling — an unnecessary crisis created by the Republicans — cut nearly $2 trillion through 2021 with strict spending caps, a move that will hurt hundreds of programs serving millions of Americans for a full decade and longer.

Given the level of extortion they faced, the White House budget office and Congressional Democrats negotiated relatively well. They prevented Republicans from touching Medicare recipients, Medicaid, Social Security and other programs. (President Obama did offer to cut entitlement spending in exchange for higher tax revenues, but Republicans refused that deal.) They arranged for more than $500 billion in cuts to come from defense spending. And they did not agree to extend the Bush tax cuts, now scheduled to expire at the end of 2012.

But that still leaves major reductions in the vital category known as nondefense discretionary spending, which faces cuts of around $800 billion over a decade. That category includes education, housing assistance, transportation, public health, veterans benefits, law enforcement and courts, environmental protection and many other crucial programs.

This spending category has been the main focus of Republican pressure for decades. In the 1970s, nondefense discretionary spending represented about 5 percent of the gross domestic product; that is now down to about 2.5 percent. Over the next decade, once the new cuts go into effect, it will decline to less than 2 percent. This year’s spending bill, signed into law a few days ago, is roughly 10 percent lower than last year’s, cutting Pell grants, environmental programs and aid to desperate states. Low-income heating assistance was cut by 25 percent.

As the economist Jared Bernstein has noted, this is the category of spending that helps people move up the income ladder, providing nutritious food, improving early education and job training and putting people to work.

The precise cuts on individual programs will be determined each year by appropriators acting under the new caps. Each year’s cuts will be more painful than the last because the spending limits fail to keep pace with population growth, inflation and the needs of the economy.

This situation is the result of the Republicans’ success at shifting Washington’s focus from job creation and revenue increases to deficit reduction, at exactly the wrong time, when the economy was too weak to handle it.

The long-term deficit needs to be reduced once economic growth has returned, but only in the context of higher taxes for the rich and a careful restructuring of Medicare. Even if the Bush tax cuts expire on time, much of the $3.8 trillion that that would bring in over a decade would have to be used for deficit reduction if the caps stay in place.

All of this leaves President Obama and the Democrats with much work to do in 2012. When the 2013 budget process begins in a few weeks, they will need to protect vital investments from further cuts and start building the case for raising the spending caps.