Supplying arms of any kind to Ukraine will only encourage it to keep fighting. The violence stems from Kiev refusing to accept that its right wing declarations and violent supporters frightened the life out of ethnic Russians to the point where independence and Russian backing seemed the only safe option. Had it recognised from the start that bad government from the inception of independence, long memories of WWII atrocities and different ethnicities and cultures, made a unitary state impossible and a federated structure the only viable option, then none of the killing and civilian suffering would have happened.
Negotiations for the setting up a method of governance which calmed the fears and met the aspirations of everyone would have been tough and with a good deal of posturing but not impossible. Instead Kiev sent in troops hoping to push NATO into supporting it. This has not happened and Kiev must now sit down and cut a deal with its Eastern rebels in a much worse atmosphere of hate brought on by killing. Giving it weapons will not enable it to win its war and get back its territory. It will only guarantee a long and bloody conflict which will go on, like in Syria, until most of everything lies in ruins.
Obama understands this. Boehner does not. The Republicans will have to make up their minds whether they want to have a policy to encourage peace or whether they just want to pick a fight.