The thing about the Tea Party groups who are only interested in lower taxes for themselves is they’re part of the problem We constitutional conservatives have been all-in for no higher taxes, even those of us who aren’t affected. The Tea Party wants a coalition? Then the members best condemn in strongest terms the slaughter of the pre-born and demand that the invasion of the US be thwarted and reversed.
First of all, everyone is affected by higher taxes and spending, whether they realize it or not.
Second, I disagree with your other point. One of the reasons the left has been so successful in pushing their agenda is they learned a long time ago the power of single issue organizing. The people who run the various leftie organizations are all hard core socialists, but they don’t try to push the whole agenda with every organization. That way they can get support from people who don’t necessarily agree on their whole agenda. That allows them to add anyone who agrees on any issue to their coalition. What you suggest would eliminate anyone who doesn’t agree on all issues from supporting us on those they do.
IMHO the TEA Party was originally started as a more or less single issue (albeit a very broad issue). Some groups have become more across the board conservative issue advocates, which reduces their ability to attract people who aren’t conservative on all issues, but agree that government is too big and spends too much.