The focus will entirely on the House. Earlier this summer the Senate passed a wide-ranging, bipartisan Comprehensive Immigration bill, which has something for everyone to love and something for everyone to hate. The House's effort is one entirely of politics. Between a large block of House Democrats and a healthy minority of House Republicans, there appears to be enough votes in the House for the Senate's version of the bill to pass.
But it's never that simple. House leadership adheres to the informal "Hastert rule," named after one-time Majority Leader Dennis Hastert (R-IL). Rep. Hastert's leadership was defined by his unwillingness to put any bill on the floor of the House if it did not have the support of the majority of Republicans in the House. As the majority party, the Republicans control which bills come up for a vote. House Majority Leader John Boehner (R-OH) endorses this "majority of the majority" strategy.
The Republican leadership is using this break to poll their constituents both formally and informally. If their polling reveals that rank-and-file Republicans want CIR, then the Republicans are expected to offer a version of CIR in October that will lead to a law being passed before the end of the year. If not, expect the CIR debate to whimper along until year's end, at which point it will fade out.