It doesn’t take a political genius to see where the contest between President Obama and Mitt Romney is heading. With Rep. Paul Ryan on the Republican ticket, the campaign is looking at a full-throated debate over the future of Medicare. Are Romney and Ryan ready?

There is plenty in Ryan’s budget blueprint — and by implication, Romney’s platform — that will spark debate and controversy. The size and shape of Romney’s and Ryan’s proposed tax cuts already are under attack by Obama and the Democrats. The domestic spending cuts in Ryan’s plan have been singled out by Democrats, who say they would shred the social safety net.

But from the moment Ryan introduced his blueprint, called the Path to Prosperity, Democrats have considered his plan to fundamentally alter Medicare to be the most politically vulnerable of his budget recommendations. That’s one big reason Democrats were gleeful when the news broke late Friday night that Romney had selected the Wisconsin congressman as his vice presidential running mate.

Republicans familiar with the deliberations that led to the pick say Romney and his advisers went into this marriage with eyes open about the pluses and minuses of putting the House Budget Committee chairman on the ticket.

Ryan’s addition has brought an infusion of energy into the Republican campaign and turned Romney, in the short run, into a more invigorated candidate. And, Republicans say, Ryan has the potential to put Wisconsin in play and help get votes in other Great Lakes states.

They also note that other candidates on Romney’s short list had pros and cons. Sen. Rob Portman might have helped win Ohio, his home state, but he would have brought the baggage of having served high up in President George W. Bush’s administration. Former Minnesota governor Tim Pawlenty has been a vigorous advocate for Romney, but he would not have put his state in play and would not have excited the base they way Ryan does.

Ryan’s budget and Medicare proposals were fully weighed as Romney and his advisers evaluated the choices for a running mate, those familiar with the process said. On balance, the conclusion was that Ryan, more than any other contender, offered the possibility of elevating the debate. The view in Boston is that Romney can win a campaign on big issues but not on small ones. In that calculus, Ryan won out.

That’s not the only reason Romney ended up going with the seven-term House member. Republicans say we shouldn’t underestimate the personal chemistry and similarities in personality and makeup between Ryan and Romney — they share an essential geekiness. Ryan, like Romney, is a numbers person who likes to break down problems and solve them after digesting reams of data.

The choice, like most vice presidential selections, also was a way for Romney to say something bigger about the kind of campaign he hopes to run. In that sense, advisers say, Ryan was “Mitt’s pick, completely.”

“Stories talk about it being a bold choice,” said one senior Romney adviser, who spoke on the condition of anonymity to talk about the decision. “To me, it was a confident choice. He was very confident in himself, in Paul Ryan, in the campaign and in the direction of the campaign he wanted to take.”

Romney hopes to force the campaign into a discussion about big choices on the country’s fiscal condition, including how to reform entitlement programs such as Medicare, Medicaid and Social Security. Both Romney and Ryan have laid out proposals; Ryan’s has more detail, but both plans are missing specifics, particularly on taxes.

Republicans believe that the country is ready for that debate and will reward politicians who speak frankly about what it will take to put the budget on a sustainable path. But they have yet to win the war for public opinion on how to do it, with Medicare the most glaring example.

How much was that considered in Boston as Romney was settling on Ryan? One adviser said: “Clearly it was in the discussion. You have to have that discussion.”

A Republican strategist with some familiarity of the discussions said that “of course the campaign understood that Democrats were going to attack on Medicare if Paul Ryan were the vice presidential nominee. But they also understood that Democrats were going to attack on Medicare if he wasn’t. . . . Having someone who is steeped in it and who knows the best way to respond and prevail is an asset.”

The question is whether Romney overestimated the pluses of picking Ryan and underestimated the minuses.

The headlines in Florida over the weekend spoke to the challenge by noting the potential problem of winning over senior citizens with Ryan on the ticket. Could that make it more difficult for Romney to take a state that is absolutely crucial to his hopes of winning the election?

Ryan’s plan would not touch Medicare for those already in the system or those nearing retirement. That hasn’t stopped Democrats in the past from accusing Republicans of wanting to gut the entire program. Nor will such criticism stop over the next 85 days.

Republicans say they fare better when the debate on the future of Medicare is fully engaged and out in the open. With Ryan on the ticket, they believe, that’s more likely to happen now, rather than in the last weeks before the election in an under-the-radar campaign by Democrats using direct mail and other means.

“We are going to go on offense on Medicare,” said Ed Gillespie, a senior adviser to the Romney campaign.

The former Massachusetts governor offered the first outlines of the attack against Obama in an interview Sunday with CBS’s Bob Schieffer on “60 Minutes.” Romney accused the president of robbing Medicare of more than $700 billion to help pay for his health-care overhaul. Ryan’s plan would keep those cuts; Romney’s would restore them.

Gillespie said the campaign will focus on Obama’s Medicare cuts.

“Every senior citizen voter in Florida and every other targeted state will know that by November,” he vowed. “They’ll know that the Romney-Ryan approach is to protect current beneficiaries, those at or near retirement. . . . We like the contrast.”

Some Republicans agree that Romney can win a debate on Medicare, but others are skeptical.

“Romney and Ryan are both data-driven guys, and there’s no question they will win the intellectual argument about whether we need to reform Medicare,” said one GOP strategist, who spoke on the condition of anonymity to give a candid assessment. “But it’s a real open question about whether they can win the emotional and political one.”

Until this weekend, Romney’s campaign had been on the defensive, battered by Obama’s attacks on the candidate’s private-sector record at Bain Capital and his decision not to release more than two years of tax returns.

The belief in Boston is that the rollout of a running mate will shift and elevate the campaign debate. The next few weeks will show how prepared they are to win it.