Then he surrendered a two-set 5-3 lead against Australia's Lleyton Hewitt in Melbourne, leaving the court close to tears after a loss which proved fatal to their chances.
Switzerland have never won the Davis Cup, one of the few significant honours missing from 33-year-old Federer's trophy cabinet.
With Australian Open champion Stanislas Wawrinka also in the Swiss team, he may never have a better chance.
"As a team, we haven't had much success over the past 50 years, so people in Switzerland still talk about 20 years ago when we made the finals," world number three Federer said after Thursday's draw.
"Hopefully they'll talk about this tie in 20 years, that would be wonderful – this is the dream for us, the players."
Victory over 76th-ranked Bolelli would give the Swiss the perfect lift-off before Wawrinka takes on the mercurial Fabio Fognini - the unpredictable Italian Number one who produced a stunning defeat of Britain's Andy Murray in the quarter-final.
"The season that Stan and me have had, I think we are ready for the big occasion," Federer, who made his Davis Cup debut against Italy in 1999, said in an interview on the ITF's website.
"We are not going to shy away from it, we will embrace it. We have the opportunity to make history."
In the other semi-final at Roland Garros, France take on holders Czech Republic with captain Arnaud Clement springing something of a surprise by selecting Richard Gasquet ahead of Gael Monfils as the second singles player.
Monfils had played his way into contention to share the singles load with Jo-Wilfried Tsonga, but at Thursday's draw Clement elected for world No. 21 Gasquet to open the tie against Czech powerhouse Tomas Berdych.
French number one Tsonga will play the second singles on Friday against hard-hitting Lukas Rosol who was preferred to veteran Radek Stepanek.
U.S. Open quarter-finalist Monfils, who has moved above Gasquet in the world rankings, will play doubles with Julien Benneteau against Czech pair Stepanek and Jiri Vesely.
"I'm very excited," Clement told the ITF. "This stadium was originally built for Davis Cup, so it's a great chance."
Tsonga said he was not surprised that the Czechs had gone with Rosol rather than veteran Stepanek.
"Radek has had some good moments in Davis Cup in the past and in the Tour but now Lukas is coming hard and playing well in the Tour and I think he deserves his place in singles."
(Reporting by Martyn Herman; editing by Amlan Chakraborty and Toby Davis)
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