If it is passed in the House the Senate would be “Obligated” to vote on it??? What Planet are you living on? Do you know how many resolutions and/or bills passed by the House have been Dead on Arrival in the Senate? There is a Graveyard in the Senate of House passed Resolutions and/or Bills.
From the Compost, for what it's worth:
The NEA stipulates that if one chamber (Pelosi’s House) passes such a resolution, which it easily could do, the other (McConnell’s Senate) must act on it within a very short time period — forcing GOP senators to choose whether to support it.