(CNN) -- The government's open. Washington is back at work. House Republicans, licking their wounds, are asking themselves what's next. And President Barack Obama has thrown down the gauntlet: The top item on his agenda is immigration reform. What are the chances that the House will now move ahead on immigration? The answer will have less to do with immigration than with how the budget battle has changed the larger political dynamic in Washington. House Republicans' views on immigration are untested, and many advocates for reform believe they are implacably hostile. But the truth is Republican opinion has been evolving since the 2012 election. More and more House Republicans, perhaps the majority, know that reform is overdue and that the GOP must be part of the solution -- to remain competitive with Latino voters and because it's the right thing to do.
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Tamar Jacoby: After budget battle, GOP may be in no mood for immigration overhaul
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But many in GOP favor legal status and have been working on reforms, she says
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She says others refuse to do President Barack Obama any favor by addressing issue
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Jacoby: GOP must take ownership, provide a strong conservative approach to reform
Still, the complex dynamic that drives @placeholder in the House may have shifted somewhat in the shutdown.