A successful vote Tuesday would allow the Senate to confirm Hagel by Thursday, or possibly earlier in the week if Republicans agree.
Senate leaders are also expected to introduce their bills to replace the sequester today. Senate Democrats will push for passage for their bill that calls for billions in new taxes, but it's unclear whether the Democratic or Republican bill will be able to pass the Senate.
The resolution would create a House-administered academic contest for students around the country. It will be subject to just 40 minutes of debate, and will need a two-thirds majority to pass.
If a roll call vote is needed for the resolution, it is expected to start in the mid-afternoon.