Romney is set to campaign in Florida while Ryan was heading to Iowa, both battleground states which may decide the outcome of the November presidential election.
With campaign battle lines re-forming, surrogates for Democratic President Barack Obama took to Sunday talk shows to cast Romney and Ryan as bent on dismantling cherished entitlements like public health insurance and pensions for seniors.
But Romney and Ryan sought to portray themselves as the answer to a US economy struggling with high unemployment.
"I've got good news for you. And that is that this nation is going to come roaring back," Romney said with Ryan looking on, amid enthusiastic applause at a rally at a NASCAR stock car racing facility in North Carolina.
Romney attacked Obama as making the United States "more and more like Europe, with its "chronic high unemployment, low wage growth and fiscal calamity right at the door."
Ryan sought to make a clear contrast with Obama's team as he spoke to some 1,700 supporters inside the building while a swelling crowd of 4,000 waited outside.
"We can either stay on the path that we are on -- a nation in debt, a nation in doubt, a nation in despair, a nation of high unemployment, where we're giving our children a diminished future -- or we can change this thing and get this country back on the right track," he said.
Democrats mounted a furious counter-attack, casting Romney's choice of running mate as evidence that Republicans want to demolish social programs like Medicare, the politically sensitive public health insurance plan for seniors.
"He's the guy who's the architect of a plan to end Medicare as we know it and turn it into a voucher program and shift thousands of dollars of costs onto senior citizens," said David Axelrod, a senior Obama campaign adviser.
"He's someone who was the architect of a Social Security privatization scheme that was so out there that even George Bush called it irresponsible."
In his first public reaction, Obama called Ryan the "ideological leader" of the Republican party.
"He is an articulate spokesman for governor Romney's vision but it is a vision that I fundamentally disagree with."
Ryan, a Wisconsin congressman, is the author of a Republican budget and deficit-cutting plan that calls for deep cuts in US spending to deal with what Republicans say are unsustainable levels of US spending and debt.
The choice to put him on the Republican ticket was seen by many as a bold, but risky move that will re-focus the US presidential campaign on debt and deficit issues amid the sluggish US economic recovery.
Romney, however, put some polite distance between Ryan's plan and his own.
"I have my budget plan," Romney told CBS television's "60 Minutes" program. "And that's the budget plan we're going to run on."
On a stop in Waukesha for Wisconsinites to hail their newly anointed native son, a visibly emotional Ryan strode on stage to the beat of thunderous applause.
But he quickly wiped his eyes to slip into the role of attack dog traditionally played by vice presidential candidates.
Ryan criticized Obama for foisting "more government, more regulations, the promise of a lot more taxes on successful small businesses."
"If this president is going to do these kinds of things in a very difficult tough election year, imagine what he would do if he never has to face the voters ever again," he added.
"You know what? We're not going to find out."
Some Republicans sought to put some distance between Romney's campaign and Ryan's controversial plans, particularly the proposal to change Medicare with a voucher system.
"I think that Mitt Romney appreciates and admires the work and the ideas that Paul Ryan has done. But Mitt Romney has his own plan," said Reince Priebus, chair of the Republican National Committee, on NBC's "Meet the Press."
In recent weeks, Romney has slumped behind Obama in opinion polls, with the incumbent taking a clear lead nationally and in most of the dozen swing states that will decide the November 6 election.
A Fox News national poll out Thursday put Obama at 49 percent to Romney's 40 percent, while a CNN poll had Obama at 52 percent, seven points up on the former Massachusetts governor.
But by picking Ryan, a favorite of small government conservatives, and embarking on a four-day bus tour across battleground states, Romney hopes to gain the upper hand in the race.
© Copyright AFP Agence France-Presse GmbH - All rights reserved. This material may not be published, broadcast, rewritten or distributed. All reproduction or redistribution is expressly forbidden without the prior written agreement of AFP.