US President Barack Obama has depicted the new Republican vice-presidential candidate Paul Ryan as the "ideological leader" of the Republican Party.
Mr Obama said Mr Ryan was a "decent" man - but with a vision "fundamentally" at odds with his own.
Thousands have turned out as Mr Ryan and Republican presidential candidate Mitt Romney tour key states.
Correspondents say the selection of Mr Ryan appears to have reinvigorated the Republican campaign.
But they caution that Mr Ryan is known for radical proposals to reform government social spending, including on health care programmes, that could prove deeply unpopular among some American voters.
'Back on track'
The new Republican duo have been continuing their bus tour of swing states that will play a decisive role in the 6 November election, with stops in North Carolina and Mr Ryan's home state of Wisconsin on Sunday.
In High Point, North Carolina, the pair stopped to shake hands and exchange high-fives with thousands of supporters who lined the streets, with another 1,300 packing a stiflingly hot furniture warehouse for a rally.
It was, correspondents say, one of the best-attended Romney campaign events this year.
"We can do this. We can get this country back on track," Mr Ryan told the cheering crowd.
"We can get our people back to work. We can get our debt paid off so we can give our children a better standard of life."
"This is Day Two on our comeback tour to get America strong again, to rebuild the promise of America," a triumphal Mr Romney told another rally in Moorseville, in the same state.
As they toured, Mr Obama made his first public comments on the selection of Mr Ryan, telling a campaign fundraiser in Chicago on Sunday that Mr Ryan was "a decent man, he is a family man, he is an articulate spokesman for Gov Romney's vision but it is a vision that I fundamentally disagree with".
It might sound like standard political rhetoric but Mr Obama's choice of language was significant nonetheless, says the BBC's Zoe Conway in Washington, marking a change in the way the campaign is being fought.
Mr Ryan is a right-wing fiscal conservative with a very different vision of government from Mr Obama - and it is that difference that will now come to the fore, she says.
Mr Ryan has proposed plans to reform Medicare, a government health insurance programme for those over 65, and Medicaid, which provides healthcare for the growing ranks of poor Americans - something Mr Romney has previously described as "very much needed".
The proposals form part of a controversial Ryan-authored Republican budget plan which Democrats say seeks to dismantle key parts of the social safety-net.
Mr Romney has been careful not to say he backs the plan in its entirety, and Romney aides have insisted the presidential campaign will be fought on Mr Romney's own vision.
But senior Obama campaign adviser David Axelrod dubbed Mr Ryan's budget as "the Ryan-Romney plan", saying Mr Ryan's selection "meant to thrill the most strident voices in the Republican Party, but it's one that should trouble everybody else - the middle class, seniors, students".
The pair will now part for the next stage of their campaigning, with Mr Romney heading to Florida and Ohio while Mr Ryan goes to another key state, Iowa.
Mr Obama will also go to Iowa for a three-day tour on Monday, while Vice-President Joe Biden will visit North Carolina and Virginia.