There are other reasons to doubt that a spending cap would force Congress to finally get serious about spending. Every year, existing laws call for reductions in Medicare reimbursement for doctors and for the alternative minimum tax to expand to cover more Americans. And every year, Congress agrees to delay these, adding billions to the deficit. Just as with a spending cap, the law should force them to resolve the issues, but there always seems to be a majority in favor of pushing them further down the road.
Ultimately, though, Republicans and Democrats may not be able to agree on a spending cap for the same reason they can't agree on anything else--the two parties have drastically different views about the size and scope of the federal government. Republicans are suspicious of any cap not tied to spending, fearing that it might just lead to spiraling taxes. But Democrats are opposed to spending caps because they could lead to slashes in social services, as the costs of healthcare tend to rise much faster than GDP. Procedural changes might help them along, but if history is any guide it won't resolve the wide gulf between their philosophies.