On the second day of the World Group quarter-finals, the US secured a 2-1 lead over France in Monte Carlo and Czech Republic moved ahead by the same score against Serbia in Prague.
Argentina play their doubles against Croatia in Buenos Aires later on Saturday after each won a singles rubber on Friday.
Spain's rain-interrupted doubles rubber versus Austria on the clay at Marina d'Or was a world away from Friday's one-sided singles, when Nicolas Almagro and David Ferrer thrashed Juergen Melzer and Andreas Haider-Maurer respectively.
The visitors kept their hopes alive with a gritty doubles performance in front of the partisan Spanish crowd, fighting back from a set down and giving themselves a chance of causing an upset if they can win both of Sunday's reverse singles.
However, with world number five Ferrer and number 12 Almagro in fine form and playing on their favored surface, top-ranked Spain should still be too strong for the Austrians.
Missing clay king Rafa Nadal, who has opted out of the competition this year and is nursing a knee injury, Spain are chasing a fourth title in five years and a sixth overall since their first Davis Cup triumph in 2000.
"It's a shame because we had our chances to force a fifth set," Spain captain Alex Corretja said in an interview with Spanish television after Austria converted their fifth match point to win a thrilling fourth-set tie break 14-12.
"In the end they knew how to cope better with the interruptions and we perhaps were lacking a little in the clarity of our ideas," Corretja added.
"Tomorrow we'll be here again and, although losing the doubles was a pity, we still have two chances to win the tie." France, runners-up to Serbia in 2010, could lose at home for the first time since April 2006 after Bob and Mike Bryan, the world number one doubles pair, put the US ahead with a 6-4, 6-4, 7-6 win over Julien Benneteau and Michael Llodra.
The Bryans broke in the opening games of the first two sets and won the third-set tiebreak 7-4 to put the Americans on the verge of a first Davis Cup semi-final since 2008.
"We came in today and played a really solid match, especially on our serve," said Mike Bryan.
"Not being down a break point on serve, especially against a great team on dirt, is a great stat with us," he added. "It wasn't flashy, we just played our workmanlike doubles today." Sunday's first reverse singles will feature Jo-Wilfried Tsonga against John Isner after both won on Friday.
In Prague, there was none of the bad feeling that marred Friday's five-hour clash between Radek Stepanek and Janko Tipsarevic as the former partnered Tomas Berdych to beat Ilija Bozoljac and Nenad Zimonjic 6-4, 6-2 7,-6.
After Tipsarevic's win on Friday, Stepanek refused to shake his hand and the Serb had to be restrained by teammates before accusing his opponent of making an obscene finger gesture.
"I did not get much sleep (on Friday night) so I am looking forward to getting some rest," Stepanek said.
Argentine pair David Nalbandian and Eduardo Schwank will be hoping for some more boisterous support at the Parque Roca for their match against Marin Cilic and Ivo Karlovic.
The hosts are looking to make up for the disappointment of losing to Spain in the 2008 and 2011 finals.
