Yes, Congress will pass a bill. This type of thing happens frequently in Congress. They bicker and moan about partisan politics, and eventually change happens and bills are signed into law. The system is set up so that change must happen in a slow and painstaking way. Eventually, Congress will pass a Zika bill.
It is most likely that Congress is going to pass the bill that allows establishment of the a kitty that seeks to fight and prevent a further spread of Zika virus. As a nation we have an obligation of ensuring the world is healthy and with that I don't see how the Congress will shoot down the bill.
Republicans are so busy trying to turn over Obamacare or launch stupid investigations into Clinton that go nowhere, they never get anything done. As we get closer to elections they are also going to be wary of spending money on anything, so that they can appear to be good fiscal conservatives.
Both Democrats and Republicans said they wanted to spend money to prevent the spread of Zika, but political disagreements ultimately trumped numerous health warnings. Senate Democrats refused to support House Republican additions to the legislation that would reduce funding for Planned Parenthood, defund parts of the Affordable Care Act and reversed a ban on flying Confederate flags in military cemeteries.