Donald Trump and Hillary Clinton took a big leap toward clinching their parties' nomination for the US presidential election, soundly defeating rivals in a slew of Super Tuesday primaries. The divisive billionaire Trump weathered a barrage of attacks from fellow Republicans to win in seven of 11 states, coming within striking distance of becoming the Republican nominee to replace President Barack Obama. Clinton also racked up seven wins with her strategy of embracing Obama appearing to pay dividends. She trounced rival Bernie Sanders across a host of southern US states – Alabama, Arkansas, Georgia, Tennessee and Texas – winning big among African-American voters and reversing a 2008 primary loss in Virginia. The former secretary of state also claimed Massachusetts, in a close race. Sanders notched wins in his tiny home state of Vermont, Oklahoma, Colorado and in Minnesota. But he now trails heavily. Both Trump and Clinton signaled their focus is beginning to shift to the general election. In victory remarks, Clinton attacked Trump's pledge to "make America great again." "America never stopped being great!" she said to cheers from supporters in Miami. "It's clear tonight that the stakes in this election have never been higher, and the rhetoric we're hearing on the other side has never been lower." Trump painted Clinton – the former first lady, senator and secretary of state – as a Washington insider, who cannot address a furious electorate's desire for change. "She's been there for so long. I mean if she hasn't straightened it out by now, she's not going to straighten it out in the next four years," he said. A recent CNN/ORC poll found that both Clinton and Sanders would easily defeat Trump if the general election – set for November 8 – were held now. But few are likely to underestimate the 69-year-old Trump after his primary rout. Super Tuesday was the most pivotal day of the US presidential primary season so far, with half the Republican delegates and a third of Democratic delegates needed to win the nominations up for grabs. Trump's victories were widespread, from Alabama and Georgia in the deep south, to Massachusetts in the northeast, to the vital battleground state of Virginia. The scope and scale of the victories will sow terror among establishment Republicans, who fear the party of Abraham Lincoln, Theodore Roosevelt and Ronald Reagan could face general electoral annihilation. While Trump's rivals Marco Rubio and Ted Cruz struggled to make the case they can still win, Trump tried to defuse an intra-party feud that may be the only serious obstacle remaining on his path to the nomination. He offered an olive branch to party leaders who are fighting a rearguard action, making the case he can unify and grow the party. "I think we'll be more inclusive and more unified. I think we'll be a much bigger party," Trump said, easing up on his hallmark bombast. However, any way you look at it, it was Trump's night, as he won big and his two top rivals did well enough to stay in the race and thus keep their supporters divided, said Sabato's Crystal Ball, a political newsletter published by the University of Virginia. "Happiness for Donald Trump is a divided opposition. He's got precisely that and it's going nowhere for the time being," the newsletter said. Cruz used victories in his home state of Texas, with its bumper haul of delegates, and in neighboring Oklahoma to argue he is the only Republican who can beat Trump. He also won in Alaska, the last state to report its results. "For the candidates who have not yet won a state, who have not racked up significant delegates, I ask you to prayerfully consider our coming together, uniting," he said. Rubio won in Minnesota, fundamentally undermining his claim to be the representative of mainstream Republicanism. It was his first win of the campaign. But he ended the day in Florida – a clear signal that he wants to win his own home state, which votes on March 15. For good measure, his campaign also announced events in Kentucky, Kansas, and Louisiana, in an attempt to pre-empt questions about his future. But it might be too little too late, with polls showing Trump with a commanding lead nationwide. The CNN/ORC poll gave Trump 49 percent of support nationwide, with Rubio a distant second at 16 percent and Ted Cruz one point further behind. Rubio and Cruz may both harbor long-shot hopes that Trump fails to win enough delegate support to secure the nomination outright, leaving the convention to decide the nominee in July. They may also be betting that whoever emerges strongest from a brutal 2016 campaign would be the prohibitive favorite in four or eight years' time.