From Saddle-Creek.com:
"Cursive's lead singer/guitarist Tim Kasher has suffered a collapsed lung. The band has been forced to cancel an undetermined number of their upcoming shows. Recovery could be anywhere between one week and one month for Tim and we should know more in the next day or so. We will let you know further details at that point."
I've posted the band's current string of US and Japan tourdates with Eastern Youth below - the first few have already been cancelled, and Saddle Creek should know more about the rest of the shows soon.

06.10 Mon. Meow Meow - Cancelled Portland, OR Eastern Youth
06.11 Tue. Paradox - Cancelled Seattle, WA Eastern Youth Buy
06.13 Thu. Bottom of the Hill San Francisco, CA Eastern Youth Buy 21+
06.14 Fri. Troubadour Los Angeles, CA Eastern Youth Buy
06.15 Sat. Che Cafe San Diego, CA Eastern Youth
06.16 Sun. Glass House Pomona, CA Eastern Youth Buy
06.17 Mon. Cafe Roma - All Ages Las Vegas, NV Eastern Youth
06.19 Wed. Nita's Hideaway Tempe. AZ Eastern Youth Buy
06.20 Thu. Stop Line El Paso, TX Eastern Youth
06.21 Fri. Emo's Austin, TX Eastern Youth
06.22 Sat. Rubber Gloves Denton, TX Eastern Youth
06.24 Mon. Sokol Underground Omaha, NE Eastern Youth
06.26 Wed. Ascot Room Minneapolis, MN Eastern Youth Buy
06.27 Thu. The Globe Milwaukee, WI Eastern Youth Buy 21+
06.28 Fri. Abbey Chicago, IL Eastern Youth Buy 18+
07.12 Fri Big Cat Osaka, Japan Eastern Youth
07.13 Sat. Club Quattro Nagoya, Japan Eastern Youth
07.15 Mon. Shibuya-Ax Tokyo, Japan Eastern Youth
07.16 Tue. Shelter Tokyo, Japan Foul