Roy Halladay got a warm greeting from St. Louis fans during the red-carpet parade for the All-Star game. They chanted ‘‘We want Roy!’’ as he sat on the back of a vehicle and waved.

Get in line. The Blue Jays ace is sure to be a popular guy over the next couple weeks.

Halladay’s future is the most pressing question as baseball revs up for an intriguing second half, with muddled division races that once again could come down to the final days. General manager J.P. Ricciardi is listening to offers for the 2003 AL Cy Young Award winner, making the right-hander the biggest chip on the open market ahead of the July 31 non-waiver trade deadline.

Halladay could tip the balance in the AL East if the Yankees, Red Sox or Rays make the best offer, or boost Philadelphia’s chances of winning a second consecutive World Series. Contending teams across baseball are salivating at the thought of inserting the ace into their rotation.

‘‘Obviously, I’m somewhere that I enjoy being and have spent my entire career. There’s a lot, I think, that goes into it,’’ said Halladay, who would have to agree to any deal. ‘‘I think as a player, there’s that will to win, that will to do it in October and basically that’s what all of this has been about. I would like that chance.’’

Any number of clubs would love to give him that opportunity, including each of Toronto’s biggest rivals in the East. The Blue Jays’ division is still the toughest in baseball, showing off its top-to-bottom strength during the American League’s 4-3 victory over the NL on Tuesday night at Busch Stadium.

Tampa Bay’s Carl Crawford made a highlight-reel catch and won the MVP award. Boston closer Jonathan Papelbon got the decision and New York’s Mariano Rivera finished for his record fourth All-Star save. Even lowly Baltimore got into the act, with Adam Jones hitting a tiebreaking sacrifice fly in the eighth inning.

The Blue Jays, who dropped back after a fast start, are talented enough to hurt the division’s top teams down the stretch, even if they decide to trade their best pitcher. Boston and New York were tied for the lead heading into the final weekend of the first half, but the Red Sox won three straight against Kansas City and the Yankees were swept by the Angels.

Don’t forget about the defending AL champion Rays, either. Tampa Bay was 6 1/2 games back.

‘‘We have a small payroll. We’re always going to be underdogs, and I love that,’’ Rays slugger Carlos Pena said. ‘‘To know that we haven’t played I think up to our full potential, and we’re still in the race, is comforting.’’

The Phillies weren’t waiting around to see what the Blue Jays decide to do with Halladay. The NL East leaders agreed to a $1 million, one-year contract with Pedro Martinez over the All-Star break and are hoping the three-time Cy Young winner can help them down the stretch after a couple of minor-league rehab starts.

‘‘I still feel like this team needs a little help, very little help,’’ Martinez said Wednesday. ‘‘I think I can supply a little bit of it. I’m not going to say all of it, but a little bit of it. That’s what we’re counting on.’’

The Phillies have been hurt by injuries to their starting rotation. They already have used nine starters through 86 games, compared with seven all of last season.

San Francisco’s loaded rotation was able to stay healthy much of the first half, leading to a renaissance in the Bay Area. Powered by All-Star starter Tim Lincecum and Matt Cain, the Giants were leading the NL wild-card race and seven back of the West-leading Dodgers.

The Colorado Rockies, who fired manager Clint Hurdle in May and replaced him with Jim Tracy, won 17 of 18 during one torrid stretch in June and closed the first half with a 27-9 run to get back into contention.

‘‘The pitching has been far superior this year than it has been in past years,’’ Giants closer Brian Wilson said, ‘‘especially on our team.’’

The Dodgers’ division lead was the biggest in baseball, with tight races the norm everywhere else. Just five games separate NL Central-leading St. Louis from fifth-place Cincinnati, and the Phillies are 6 1/2 ahead of the fourth-place New York Mets in the East.

‘‘It’s kind of a unique year,’’ Houston manager Cecil Cooper said. ‘‘There are a lot of teams close and in the hunt. Aside from just our division, everybody’s bunched together pretty good.’’

The division leads of the AL’s top teams add up to a paltry eight games. In addition to the tight East, the Los Angeles Angels are 1 1/2 games ahead of Texas in the West and Detroit leads the Chicago White Sox by 3 1/2 games in the Central.

All those cloudy races caught the attention of the nation’s first fan at the All-Star break.

‘‘What’s been interesting about baseball this year, other than the Dodgers, who’ve been playing terrific ball, there’s a lot of parity,’’ President Barack Obama said. ‘‘It means everybody around the country has a little bit of hope for their team.’’