ATLANTA — Establishment Republican Thom Tillis’ victory in the Senate primary in North Carolina has spurred both sides to draw battle lines that could frame Senate races across the nation.

After dispatching several tea party and Christian-right rivals on Tuesday, Tillis quickly cast Democratic Sen. Kay Hagan as an acolyte of President Barack Obama. Hagan countered just as fast, painting the speaker of the North Carolina House as the face of Republican extremism.

It’s a strategic model that could help determine who controls the Senate after November, with similar themes playing out in Arkansas, Colorado, Georgia, Louisiana and Kentucky. Whether Republicans can gain the six seats required to control the 100-member chamber will have an impact on Obama’s influence during his final two years in the White House as well as his legacy.

Hagan is one of the Democrats’ most vulnerable incumbents, in part because she voted with Obama and Majority Leader Harry Reid on health care, fiscal issues and more.

“Kay Hagan and Harry Reid are nothing but an echo chamber for President Obama’s worst ideas,” Tillis told supporters Tuesday night, moments after drawing about 46 percent of the vote, eclipsing the 40 percent required to win without a runoff.

The return fire was swift, stinging and extensive. Hagan described Tillis’ North Carolina as a place where voting is harder, health care for women is less available, and fewer state dollars are spent on education.

“Speaker Tillis,” Hagan said in a statement, “cut public education by nearly $500 million, killed equal pay legislation, defunded Planned Parenthood, gutted unemployment insurance for 170,000 people and rejected health care for 500,000 North Carolinians” by not expanding Medicaid under Obama’s health care law.

State Republicans also made it harder to vote and refused teacher pay raises, said Hagan, who called herself the only candidate in the race who will represent North Carolinians.

The Hagan campaign published a memo that included some of Tillis’ more incendiary statements, including when he suggested that teachers “only care about their jobs and their pensions” and when he said that conservatives must “find a way to divide and conquer” individuals on public assistance by making truly needy citizens “look down at these people who choose” dependency.

Tillis casts his legislative record as commonsense conservatism that appeals to voters in this closely divided state, which Obama won in 2008 but lost in 2012. Tillis used that record to corral endorsements from mainstream powers like the U.S. Chamber of Commerce and former Florida Gov. Jeb Bush, while attracting enough tea party and archconservative support to avoid a runoff that would have highlighted GOP divisions.

The themes emerging in the first 24 hours of North Carolina’s general election reflect the national campaigns run by each party in the 2014 midterms. Republicans bet they can parlay voter discontent over Obama’s health care law, the economy and the nation’s overall direction — particularly among independents and conservatives who typically dominate midterm elections — into victories over Hagan, Louisiana’s Mary Landrieu and other Democratic incumbents like Arkansas’ Mark Pryor and Colorado’s Mark Udall.

Hagan, Pryor and Landrieu are running for the first time since they supported the Affordable Care Act — votes already exploited via millions of dollars in television advertising by their opponents. They hold three of the seven seats Democrats must defend in states Obama lost in 2012 and where he remains broadly unpopular.

“If we continue on this trajectory that we’re on, it’s virtually impossible for Democrats to overcome all of that,” said Wes Anderson, a Republican pollster whose firm produces Tillis’ television spots.

Democrats pitch themselves as pragmatic problem solvers more in tune with voters than their Republican rivals. And they have their own polls to fall back on. Congress — the House is controlled by Republicans and the Senate by Democrats — is more unpopular than Obama, and a majority of voters prefer changes to Obama’s health care law over the full repeal pursued by the House GOP.

Democrats’ national Senate campaign office regularly criticizes House Republicans running for the Senate — Cory Gardner in Colorado, Tom Cotton in Arkansas, Bill Cassidy in Louisiana — for opposing equal wage laws, approving more abortion regulations, blocking minimum wage hikes and unemployment benefits, and voting more than four dozen times to repeal the health care law.

In Colorado, a Udall ad highlighted Gardner’s staunch anti-abortion stance as “disturbing.” Gardner backed off his previous support for a so-called personhood amendment that would grant fetuses legal rights from conception.

Arkansas’ Pryor has hammered Cotton for opposing the farm bill, accusing the Republican of hurting Arkansas farmers.

Landrieu, seeking a fourth term, has mostly left the attacks on Cassidy to others while she plays up her seniority and plum chairmanship on the Senate energy committee, which she casts as a boost for Louisiana’s oil and gas industry.

In Georgia, Democrat Michelle Nunn awaits a Republican nominee for a GOP-held open seat, but she regularly tells voters that all of her potential rivals, including three House members, “are running to extremes.”

Senate Minority Leader Mitch McConnell still has to get past a GOP primary in Kentucky, but Democrat Alison Lundergan Grimes has for months been running against him. On Friday, she launches a bus tour inspired by McConnell’s remarks to a local newspaper that creating jobs in Kentucky is “not my job.” He says he was misquoted, and this week launched a statewide TV ad touting his record of protecting jobs.

Nunn and Grimes must defend themselves from attacks that their campaign accounts are flush with money from liberal backers from outside their respective states — proof, Republicans say, that they’ll be automatic votes for Obama and Reid.