Taurasi's status is unclear going into Tuesday night's game in Tulsa as the Mercury try for a ninth straight victory over the Shock.
Phoenix learned it would be without Taylor for the year after she suffered a torn ACL in April. She was second on the team with 16.7 points per game last season while helping to facilitate the WNBA's highest-scoring offense.
The Mercury, however, didn't anticipate opening 2012 without Taurasi, who was a late scratch Sunday with a strained hip flexor. Without its leaders, Phoenix lost 105-83 to Minnesota.
Taurasi is day to day, with the Mercury's official website saying the decision to sit her was precautionary. Taurasi missed two games last season with back spasms, but led the league with 21.6 points per game.
"When she's in, it's kind of like she just settles everyone down a little bit. She's kind of like a safety valve," said rookie Samantha Prahalis, who had 12 points and six assists but also four turnovers in her debut.
Coach Corey Gaines said in the preseason that his team hoped to improve defensively after giving up a league-high 86.0 points per game last year, but the Lynx shot 57.1 percent and outrebounded the Mercury 40-28.
Phoenix lost its first three games last season and is trying to avoid another early deficit in the Western Conference. A matchup against Tulsa should help that cause.
After going a league-worst 3-31 last season, the Shock opened 2012 with an 88-79 loss to San Antonio on Saturday.
Tulsa, which lost its final six games last year, was without two of its top three scorers from 2011. Tiffany Jones (formerly Jackson), who averaged a team-high 12.4 points, is pregnant and will miss the season, while Elizabeth Cambage (11.5 ppg) won't join the team until after the London Olympics.
Former Mercury guard Temeka Johnson scored 21 points Saturday and Ivory Latta added 14 off the bench, but the Shock allowed the Silver Stars to go on a 15-2 run over the final 2:33.
"We have a young team and it's going to be a work in progress," coach Gary Kloppenburg said. "Our kids played extremely hard and gave themselves a chance to win. We just couldn't execute at both ends in the last 10 minutes."
Tulsa was the lowest-scoring team in the WNBA in 2011 with 69.2 points per game while giving up the second-most at 82.1.
Phoenix has won eight in a row against Tulsa since a loss in 2009 when the Shock franchise was in Detroit. Taurasi averaged 18.3 points in the season series in 2011, never playing more than 26 minutes as the Mercury won the four meetings by an average of 21.0 points.