There are moments in American political history when one of the two major parties finds itself badly out of step with the middle, so beholden to its base that it cannot appeal to the centrist voters who decide most elections. What comes next is a series of predictable steps: Lose a few elections, hit the political equivalent of rock bottom, then turn control of the party over to a relative centrist who can recast the party in a new light.

It happened to Republicans when Sen. Barry Goldwater (R-Ariz.) won only six states, and 38.5 percent of the vote, in 1964; four years later, the party nominated Richard Nixon, one of the more liberal Republican presidents of the 20th century. It happened to Democrats twice, in 1972 and 1988, when liberal nominees George McGovern and Michael Dukakis lost badly; the next presidential cycle, Democrats picked Southern governors from the centrist wing of the party, both of whom won.

After two straight losses in presidential elections and some of the worst poll ratings ever recorded, the Republican Party again finds itself at a fork in the road. One faction, the older, more established wing of the party, wants to travel the middle path, in hopes of appealing to unaffiliated voters. The other faction, younger, brasher, more ideologically rigid, believes that the party has lost its way, and that only the rightward path leads back to electoral success.

Who is the Republicans’ next Barry Goldwater? At what point does the GOP hit rock bottom? Here, in chronological order, are four moments when that point could (or could have) happened:

1) Mitt Romney and Todd Akin: In a different world, the GOP’s nadir might have come in 2012, the year Democrats demonstrated that they have a winning national coalition of Hispanics, African Americans and white, college-educated women. Mitt “self-deportation” Romney scored lower than both John McCain and George W. Bush among Hispanics, and Akin and Indiana Senate candidate Richard Mourdock hurt their party among women voters.

The most conservative, and the most optimistic, Republicans hope Romney, who never thrilled the Republican base, and flawed Senate candidates such as Akin were the bottom, and that there’s nowhere to go but up.

Based on poll numbers and the inability of House Republican leaders to control their flock, it’s clear that 2012 wasn’t the turning point most leaders hoped. The White House rightly believes that House Speaker John Boehner can’t deliver votes, and the current spat over the government shutdown and the debt ceiling demonstrates that the conservatives in the House can derail any deal Boehner might make with President Obama.

Meanwhile, a new Washington Post/ABC News poll shows almost three-quarters of Americans disapprove of the GOP’s handling of those budget negotiations. Poll numbers that scary might have been an impetus for change in the past. The fact that those numbers aren’t scaring Republicans now shows that those conservatives don’t believe they’ve hit bottom just yet.

Q: Do you approve or disapprove of the way Republicans in Congress are handling negotiations over the federal budget?

2) Ken Cuccinelli: In Virginia, conservatives got what they wanted in Cuccinelli: An unabashed defender of just about every one of their issues. Now, just a few weeks out from Election Day, party strategists are already casting blame for Cuccinelli’s disappointing campaign; nine recent polls have shown Cuccinelli trailing Democratic nominee Terry McAuliffe — hardly the most likeable candidate himself.

How could Republicans lose a swing state, which was supposed to lean their way in a low-turnout, odd-numbered year? Cuccinelli’s unapologetic conservatism is partly to blame. So is Gov. Bob McDonnell’s (R) dealings with a contributor, and the government shutdown, which voters blame on Republicans more than Democrats. But even without the shutdown, Cuccinelli pursued the same path that led to Romney’s defeat in 2012: He attacked, and attacked, and attacked again, without offering his own vision for Virginia.

Simply being the Party of No is no way to win an election. If that’s the message Republicans take from Cuccinelli’s campaign, they can salvage something from the wreckage of a campaign they should have won.

3) Disastrous Senate nominees: Over the last two cycles, Democrats have won at least five Senate contests against Republican nominees who beat more electable establishment choices in a primary. If Sharron Angle, Christine O’Donnell, Ken Buck, Akin and Mourdock had lost their primaries, Republicans would control the Senate today.

There are hints that history could repeat itself. Republicans worry that if Senate Minority Leader Mitch McConnell loses his primary, his seat would flip to Democratic control. Divisive Republican primaries in Georgia and Alaska, and possibly even Louisiana, could give Republicans more subpar nominees.

Conservative groups in Washington advocate for hard-line nominees. Establishment groups in Washington care more about the first vote a new senator would take — to elect McConnell, or some other Republican, as majority leader — than any subsequent vote that senator casts. The conservative groups have won more primary fights than they’ve lost in recent years; the party’s base may not like a squishy vote, but losing Senate seats they should have won, for a third cycle in a row, might provide party elders the impetus to win back some of the conservative voters for whom the establishment label has been a kiss of death.

4) 2016: If Republicans want their chance to actually nominate a hard-liner like Goldwater, they’ll have the option in 2016. Sens. Ted Cruz (R-Texas) and Rand Paul (R-Ky.) are the two most visible potential presidential candidates in the GOP today. Most other potential candidates — notably Louisiana Gov. Bobby Jindal (R) and Sen. Marco Rubio (R-Fla.) — are working to position themselves alongside Cruz and Paul, rather than separating themselves.

Google searches over the past 12 months:

Whether it’s New Jersey Sen. Chris Christie (R) or Rep. Paul Ryan (R-Wis.) or Wisconsin Gov. Scott Walker, there will be a moderate alternative, though that candidate will hate the label (“Pragmatic conservative” will be the favored nomenclature). But if the party base isn’t convinced that losses in 2012, 2013 and maybe even 2014 are reason enough to change, then the conservative candidates will have the edge.

Democrats have built their winning coalition; if it takes one more presidential cycle to prove that to base Republican voters, their 2016 nominee could finally lead to a Barry Goldwater moment.