WASHINGTON — House Republicans are preparing to unveil their own broad template for overhauling the nation’s immigration system this week, potentially offering a small opening for President Obama and congressional Democrats to pass bipartisan legislation before the end of the year.

Speaker John A. Boehner of Ohio and other Republican leaders are expected to release a one-page statement of immigration principles this week at their annual retreat in Cambridge, Md., according to aides with knowledge of the plan. The document is expected to call for border security and enforcement measures, as well as providing a path to legal status — but not citizenship — for many of the 11 million undocumented immigrants in the country, the aides said.

The Republican effort comes as Mr. Obama is expected to push once again for an overhaul of the immigration system in his State of the Union address Tuesday, and as lawmakers from both parties describe immigration as one of the few potential areas for bipartisan compromise before the end of the current Congress.

“The principles they lay out I’m sure won’t satisfy everybody,” Michael R. Bloomberg, former mayor of New York City, said at an immigration forum on Friday. But, he added, “if we can make some compromises here for the good of the country, I think we have a very good chance for the first time in a long time of changing something that is really damaging all of us.”