As Republicans Mitt Romney and Paul Ryan campaigned together Sunday, President Obama and his Democratic allies ramped up their effort to make sure their rivals remain joined at the hip by tightly tethering Romney to his running mate’s “radical” ideology.

Obama made his first public remarks about Romney’s choice of Ryan, the Wisconsin congressman, as his vice presidential candidate during remarks at a fundraising event here. The president called Ryan the “ideological leader of Republicans in Congress,” prompting a crowd of hundreds at the Bridgeport Arts Center to boo.

“No, no,” Obama said. “I know him. I welcome him to the race. He’s a decent man, a family man, an articulate spokesman for Governor Romney’s vision. But it’s a vision I fundamentally disagree with.”

If Romney is betting that his selection of Ryan will rally his conservative base in a nip-and-tuck election, Democrats are counting on its having the same effect on their side. For months, the Obama campaign has been trying to tie Romney to Ryan’s Republican House budget proposal, which the president in April called “social Darwinism” that would pit the poor against the wealthy. Ryan has proposed major cuts to spending and entitlement programs in an effort to curb the spiraling national debt.

But Obama’s campaign believes Ryan’s ideological views will turn off moderate voters and drive liberals to the polls, especially in Florida, an important swing state where Obama, in two appearances last month, vilified the congressman’s proposal to partially privatize Medicare. In this way, Democrats say, Ryan provides a natural foil for the president, who has framed the election as a choice between sharply contrasting visions that could fundamentally reshape the nation.

At the fundraising event, one of five Obama attended in Chicago on Sunday, the president said of his rivals: “They all believe that if you get rid of more regulations for big corporations and give more tax breaks to the wealthy, it will lead to jobs and prosperity for everyone else. That’s what they’re proposing, where they’ll take us if they win. That’s not speculation; it’s on their Web site, in their budget that House Republicans voted for repeatedly.”

Responding to Obama’s remarks, Romney spokesman Ryan Williams charged the president with running a “fear and smear campaign because his policies have failed.”

With Ryan, considered a policy wunderkind inside the GOP, on the ticket, Williams said the Romney campaign will “continue to put forward idea after idea on how to grow the economy and get spending under control.”

Yet beneath the Obama reelection team’s forceful response to Ryan was a sense of delight at the campaign headquarters in Chicago, and among their Democratic allies, that they got the vice presidential candidate they wanted.

While Ryan may help Romney take the focus off his undisclosed tax returns and tenure at Bain Capital, at least temporarily, and return the debate to the budget and economy, the congressman also presents an opportunity for Democrats who believe Americans have grown frustrated with an increasingly ideological and rigid Republican Party.

“He was the one nominee who could actually do damage to the ticket,” said Bill Burton, a co-founder of Priorities USA Action, a super PAC that supports Obama. “Everybody else was fairly neutral. No doubt he will fire up conservatives, but he also comes with so many liabilities from his budget that Romney will come to think he made a sizable mistake attaching himself so closely to Paul Ryan.”

Obama campaign manager Jim Messina referred to Ryan as a “radical” in a statement on Saturday, and other Democrats already have begun to use Ryan in their fundraising solicitations, warning supporters of his appeal to far-right conservatives who will throw money at the Romney campaign. Obama’s five fundraising events Sunday were expected to take in at least $6.4 million as the president attempts to keep pace with Romney, who has outraised him the past three months.

On the other side, Republicans believe Ryan will put Obama on the defensive over the spiraling national debt. Obama has centered his campaign on an appeal to the middle class, emphasizing his belief that the federal government should play a role in investing in public needs such as infrastructure, education and health care.

But Republicans have accused him of allowing the deficit to grow while pumping money into government programs, such as the stimulus package and the health-care overhaul, without fully energizing the economy. In responding to past criticism from Obama over Ryan’s Medicare proposals, Romney and other Republicans have charged that the president’s health-care plan moves $700 billion from Medicare to pay for other health-related programs.

David Axelrod, the president’s senior campaign adviser, defended Obama against those charges Sunday, noting on ABC’s “This Week” program that Ryan incorporated the same $700 billion cut into his budget proposal.

“The difference is that the president is trying to strengthen Medicare,” Axelrod said. “Under the changes the president made, seniors are getting more prescription coverage and preventative care. . . . The Romney-Ryan plan would not do that. In fact, by turning it into a voucher program . . . ultimately they’re going to shift thousands of dollars onto the backs of seniors and Medicare itself will be in a death spiral.”