ATLANTA — With the walloping Republicans gave Democrats in the midterm elections, the GOP stands one Louisiana Senate runoff away from completely controlling Southern politics from the Carolinas to Texas. Only a handful of Democrats hold statewide office in the rest of the Old Confederacy.

The results put Southern Republicans at the forefront in Washington — from Senate Majority Leader-in-waiting Mitch McConnell of Kentucky to a host of new committee chairmen. Those leaders and the rank-and-file behind them will set the Capitol Hill agenda and continue molding the GOP’s identity heading into 2016.

In statehouses, consolidated Republican power affords the opportunity to advance conservative causes from charter schools and private school vouchers to expanding the tax breaks and incentive programs that define Republican economic policy. The outcome also assures that much of the South, at least for now, will remain steadfast in its refusal to participate in President Barack Obama’s health care overhaul.

“I think these new leaders can help drive the conservative movement” at all levels, said Louisiana Republican Party Chairman Roger Villere, echoing the celebrations of Republican leaders and activists across the region. “We just want a government that doesn’t suppress people.”

Republicans widely have acknowledged that the party now has to prove it can govern. But one-party rule invariably means internal squabbles. Republican White House hopefuls in particular must court Southern Republicans who are more strident than the wider electorate on issues ranging from immigration to abortion and the broader debate over the government’s role — and how to pay for it.