DENVER — Human nature and politics being what they are, Republicans will underestimate the trouble they’re in, and Democrats will be eager to overestimate the strength of their post-2012 position.

Begin with the GOP: As Republicans dig out from a defeat that their poll-deniers said was impossible, they need to acknowledge many large failures.

Their attempts to demonize President Obama and undercut him by obstructing his agenda didn’t work. Their assumption that the conservative side would vote in larger numbers than Democrats was wrong. The tea party was less the wave of the future than a remnant of the past. Blocking immigration reform and standing by silently while nativist voices offered nasty thoughts about newcomers were bad ideas. Latino voters heard it all and drew the sensible electoral conclusion.

Democrats are entitled to a few weeks of reveling because their victory really was substantial. Obama won all but one of the swing states and a clear popular vote majority. The Democrats added to their Senate majority in a year that began with almost everyone predicting they’d lose seats. They even won a plurality of the vote in House races; Republicans held on because of gerrymandering.

Just as important, the voters repudiated the very worst aspects of post-Bush conservatism: its harsh tone toward those in need, its doctrinaire inflexibility on taxes, its inclination toward extreme pronouncements on social issues, and its hard anti-government rhetoric that ignored the pragmatic attitude of the electorate’s great middle about what the public sector can and can’t do. If conservatives are at all reflective, we should be in for a slightly less rancid and divisive debate over the next couple of years.

Yet Obama and his party need to understand that running a majority coalition is difficult. It involves dealing with tensions that inevitably arise in a broad alliance. Democrats won because of huge margins among African-Americans, Latinos and Asians, but also because of a solid white working-class vote in states such as Ohio, Michigan and Pennsylvania, particularly from union members. Obama needs to think about economic policies that deliver benefits across this wide spectrum of less well-to-do Americans. A longing for balanced budgets is not what drove these voters to the polls.

At the same time, there was a substantial middle- and upper-middle-class suburban component of the Democratic coalition that is moderate or liberal on social issues and sees the GOP as backward-looking. Many voters in this group bridle at sweeping anti-government bromides because they care about essential government functions, notably education. But they are certainly not classic New Deal or Great Society Democrats.

Such voters are central to what has become known as the “Colorado strategy.” It’s a view that the Democrats’ long-term future depends on moderate, younger and suburban voters, especially women, combined with the growing Latino electorate. And in Colorado itself, this strategy worked exactly as advertised.

As Curtis Hubbard, The Denver Post’s editorial page editor, noted, Obama won big in the party’s bastions in Denver and Boulder. But he also won Jefferson and Arapahoe counties, key Denver-area swing suburbs, and, a bit farther away, in Larimer County around Fort Collins. The Democrats’ victory here had depth: The party recaptured the state House of Representatives while holding the state Senate.

Managing a coalition that includes African-Americans, Latinos, white working-class voters and suburbanites in the new and growing metro areas will take skill and subtlety. And Democrats need to recognize that some of their core constituencies — young people, African-Americans and Latinos — typically vote in lower numbers in off-year elections. The party requires a strategy for 2014.

But these are happy problems compared with what the GOP and the conservative movement confront. They need to rethink their approach all the way down.

Many conservatives seem to hope that a more open attitude toward immigration will solve the Republicans’ Latino problem and make everything else better. It’s not that simple. For one thing, a more moderate stand on immigration could create new divisions in the party. And its weaknesses among both Latinos and women owe not simply to immigration or to social issues, respectively, but also to the fact that both groups are more sympathetic to government’s role in the economy and in promoting upward mobility than current conservative doctrine allows.

A party that wants to govern has to do more than run against government. For the right, this is the inconvenient truth of 2012.

E.J. Dionne’s e-mail address is ejdionne(at)washpost.com.