In reality what would the benefits to swing states be? And if it's substantial enough to get Biden a boost then why would Republicans help this package through Congress?
You're right about why would the Republicans get it through Congress. But there's splits and political paralysis in the US. The Empire's hegonomy is crumbling, and it has become a pariah state over Palestine, which is causing further paralysis. The Global South won't follow the US over sanctions against Russia, it's lost that area for influence. This is further compounded by Palestine, greater making it a pariah state, again leading to splits and paralysis. Warmongering is the name of the game and I think the warmongering Republicans what that more than anything. Hence, Pence throwing in the towel is significant. The survival of the US Empire is more important to the political class than party politics. Because isn't the US party politics all about the US Empire's interests in the world.
There are those saying ditch Ukraine and solely concentrate on Palestine because they know they can't fight on two fronts. Others are saying no, we need three front fight Russia, China Iran. Russia they'be got proxies to do it, so no US body bags. China, they're busy trying to get an alliance going to do the dirty work, Australia, South Korea and Japan and others, to take on China. Still no US body bags. Iran is the real goal around the Palestine issue for the US. The colonial occupiers are their proxy warmongers and have always been. But, it's not looking good for their proxies in Israel as the Arab and Muslim world have become inflamed. The Vietnam syndrome kicks in and it resulted in US further direct involvement, after the French lost the will to fight because they had other issues to deal with. The US will be forced to get further involved, than the military sdvisors already in Palestine, if it's start to goes belly up for Netanyahu.
Ukraine is dispensable for the US Empire. There are bigger issues to deal with. Palestine being the immediate troubling issue for them.