http://www.reuters.com/article/2013/06/26/us-usa-immigration-idUSBRE95P0ZX20130626
Final passage came on June 27th with a vote of 68 to 32, with 14 Republicans backing the bill:
http://www.cnn.com/2013/06/27/politics/immigration
In the last few weeks, House Speaker John Boehner has repeatedly said that the House would not take up the Senate bill, and would come up with it's own, and today, GOP House members met to discuss how they would move forward. Some media outlets have gone so far as to say that immigration reform is dead in the House, but that seems to be hyperbole for now as argued by John Ward of the Huffington Post "Immigration Doom And Gloom Is Giving John Boehner Some Room To Operate ":
http://www.huffingtonpost.com/2013/07/10/immigration-john-boehner_n_3573669.html
My own expectation is that the House will work towards passing legislation to give a path to citizenship for DREAMers, a STEM bill that will increase visas for skilled immigrants and allow those who earned advanced degrees to stay in the U.S., and of course, border security. Of course, the House has already voted to stop Obama's DACA executive order: http://www.thonline.com/news/national_world/article_86eea608-45fa-562f-84a7-66e5414dfb6e.html and a DREAM act was supposed to be introduced by democrats in the House earlier this year: http://www.huffingtonpost.com/2013/02/07/dream-act_n_2639187.html (apparently this did not happen) but this legislation would give House Republicans a way to deal with one of the more sympathetic groups of undocumented immigrants, without having to deal with a broader "amnesty."
In the meantime, President Obama is pushing the House to take up the Senate bill ("or similar legislation"):
http://www.reuters.com/article/2013/07/10/us-usa-immigration-obama-idUSBRE96908Z20130710
and former President Bush called for a "positive resolution to the debate":
http://www.cnn.com/2013/07/10/politics/bush-immigration-speech/index.html?hpt=po_c1
