Not enforcing the law cannot be defunded, because not doing something costs no money. It may be possible to stop the government from giving official documentation to a certain class of people, but that does not stop Obama from ordering ICE to not enforce the law for that class of people. The lack of enforcement will encourage and enable a lot more illegal aliens to come to America.
The only way to deal with a president, who blatantly refuses to enforce the law or follow the Constitution is impeachment, conviction and removal. Anything less is a half-measure, too little and too late.
If there are not enough votes in the Senate, that is only because the Republicans do not really care and have not made the case to the American people. The Republican establishment dearly wants an Amnesty and the only way they can get it is via a dictated amnesty from Obama. Do not expect this bunch of corrupt and traitorous Republicans to move on this. The fix is already in. The leadership is much influenced by financial interests that want amnesty.