Valcke and Bach have similar concerns: Both mega-events face delays, there is increased public scrutiny over the billions in public money being spent and, in the case of the World Cup, time is short.
Valcke will be in Sao Paulo on Monday, and visit Cuiaba, Manaus and Natal. The World Cup opens on June 12 in Sao Paulo, but the stadium there won't be ready until April. Others also face tight deadlines.
The late finish means a rush to install television equipment, few test games, and little time to physically count seats and make sure they match the tickets.
"The big difficulty is that we don't have a training period," Valcke explained in a recent interview on France Bleu radio. "That's to say we can't train ourselves. We find ourselves with stadiums as was the case at the Confederations Cup that are delivered too close to the kick-off of the first match, and stadiums where we have encountered a certain number of difficulties. We find ourselves with infrastructure that isn't perfectly in place."
Valcke has pressed Brazilians for two years to speed up. At one point he told Brazil organizers bluntly: "You have to push yourself, kick your (backside)."
Brazil is spending about $3.6 billion on 12 new and renovated stadiums, and the cost is rising. The original budget for stadiums was $1 billion. Government officials at first promised stadiums would be built with only private money. Instead, 80 percent has been public money.
In addition to stadiums, World Cup-related construction will cost at least three times that much. And four of the stadiums in Brasilia, Natal, Cuiaba and Manaus are likely to become white elephants with no top teams in those cities.
"This (Brazil) is the Mecca of football," Valcke said. "Even though we've been through, and are going through phases that are a bit complicated and tense between Brazil and us because not everything is ready it's clearly the World Cup that all football lovers dream of. ... There will certainly be problems. There will be problems because it's a country the size of a continent."
Trouble spots include: Soaring hotel prices, questions about air travel through Brazil's outdated airports, and the promise of daily demonstrations aimed at the billions being spent in a country with severe social inequality.
Bach has said Rio doesn't have "a single moment to lose."
Major General Fernando Azevedo e Silva, appointed three months ago to coordinate government spending for the Olympics, underlined its urgency. In a recent interview he compared stepping into his new job to "changing tires on a car that's moving."
After months of their own delays, Rio Olympics organizers are expected to announce an operating budget by the end of the month. The original 2009 bid document showed the operating budget at $2.8 billion, but initial bids always vastly underestimate the costs.
The operating budget is only for running the 2016 games. About $11 billion more in public and private money will be spent on games-related projects.
Disagreements over the budget have gone on for months, with national, state and local governments debating who pays what. This is also an election year with Rousseff facing voters in October.
Public spending on the World Cup and Olympics has become sensitive since protests last year during the Confederations Cup. Concern has also spiked about water pollution at Olympic venues for sailing, canoeing, rowing and distance swimming.
Olympic medal winners at a recent event in Guanabara Bay said it was the dirtiest water they'd ever experienced.
Chief Operating Officer Leo Gryner said in August that $700 million in public money would be needed to balance the operating budget. Since then Chief Executive Officer Sidney Levy, who took over a year ago, said the $700 million would not be needed with some new income expected from local sponsorships.
AP writer John Leicester in Paris contributed.
Stephen Wade on Twitter: http://twitter.com/StephenWadeAP