Fans can cast their votes until 3 p.m. CT on Friday.
"It's a little complicated to go through another round [of voting], but I'm going to keep playing and am excited [for the possibility of being] in that kind of rotation," Martinez said through a translator. "I feel I belong there. If I don't make it, I'm just happy to be in that situation."
The Cardinals have already reached out to the Royals to propose a joint "Show Me State" campaign for Martinez and Kansas City third baseman Mike Moustakas, an American League Final Vote candidate. Martinez also hopes to garner support from his home country, the Dominican Republic.
"I'm hoping the people in the Dominican help me in the competition," said Martinez, who is up against a pair of countrymen in Cueto and Familia.
Martinez, in his first season as a full-time starter, has put up numbers that are more than deserving of strong All-Star consideration. He ranks fifth in the NL with 13 quality starts, ninth with a 2.70 ERA and 10th with 105 strikeouts. Fourteen of the 30 earned runs he has given up came during a two-start stretch in early May. Take those away, and he has an ERA of 1.58 over his other 15 starts.
"Carlos is really just getting on the map here," manager Mike Matheny said. "I think the fact that he's in those discussions right now is a huge compliment to him. You never know how this can play out."
Martinez has also ascended to All-Star worthiness in a season that he has dedicated to the memory of his late teammate and friend, Oscar Taveras. No one with the Cardinals was more shaken by Taveras' death during the offseason, though Martinez reported to Spring Training believing that life's adversity has helped him mature. He wears No. 18 to honor Taveras.
If Martinez wins the Final Vote, he'll join teammates Jhonny Peralta, Matt Holliday, Trevor Rosenthal, Michael Wacha and Yadier Molina next week in Cincinnati.
"To all you Cardinal fans out there, you have to start voting him in," Wacha said. "I'm excited for him, and he's very well deserving. I hope he can make it to Cincinnati."
Martinez is the third Final Vote candidate the Cardinals have had since the contest began in 2002. Albert Pujols was up in the inaugural vote and finished fourth. David Freese won in 2012 to become a first-time All-Star.
Voting is open now at MLB.com to select the final player for each League's 34-man roster via the 2015 Esurance MLB All-Star Game Final Vote.
During the Midsummer Classic in Cincinnati on Tuesday, July 14, fans can once again visit MLB.com to submit their choice for the Ted Williams Most Valuable Player Award presented by Chevrolet. Voting exclusively at MLB.com, online and via their mobile devices in the 2015 All-Star Game MVP Vote presented by Chevrolet, the fans' collective voice will represent 20 percent of the overall vote that determines the recipient of the Arch Ward Trophy.
MLB.TV Premium subscribers will be able to live stream the All-Star Game via MLB.TV through FOX's participating video providers. Access will be available across more than 400 supported MLB.TV platforms, including the award-winning MLB.com At Bat app. MLB.com will provide extensive online coverage of the All-Star Week festivities, including the 2015 Gillette Home Run Derby presented by Head & Shoulders, part of Gatorade All-Star Workout Day on Monday, July 13. The Derby will feature a new format with brackets and timed rounds and will be broadcast live by ESPN and MLB.com beginning at 7 p.m. ET.
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