Eighteen House Republicans plus the House Democrat caucus is not a Republican coalition. You are describing a Democrat coalition, as in the Texas legislature.
If the people want the individual mandate delayed badly enough, the votes will materialize. That is the objective of Cruz and the Tea Party caucus.
Politics is about inspiring, leading and shaping public opinion, not counting legislators.
I disagree. Politics in a Representative Republic is about inspiring, leading and shaping public opinion so you can win elections and get the legislators to count. The time to do that is BEFORE the election, because if you and your allies don't win the election, you don't get to pass what you want passed.
President Reagan first won the election, then got done some of what he wanted. President Obama first won the election and is now getting done some of what he wanted. In neither case did they do that by only sticking to their 100% allies, they formed coalitions. As the great President Reagan said: "The person who agrees with you 80 percent of the time is a friend and an ally — not a 20 percent traitor."