David Frum redefines the Republican coalition not as a three-legged stool but as a four point... something:

Today though it’s more relevant to think of conservatism as an attempt to draw a line connecting four points:

1) No tax increase
2) No defense cuts
3) No Medicare cuts
4) Rapid move to a balanced budget.

Obviously it’s impossible to meet all four of those commitments. It would be difficult enough to combine #4 with even two of the first three.
Much of the struggle within the conservative world can be understood as a quiet debate over which of those commitments to jettison.
The dominant group within CPAC for example would gladly jettison #2 and is less than enthusiastic about #3. When the Values Voters Summit convenes in October, you’ll see that its attendees are ready to jettison #4 and are less than 100% committed to #1.
Much of the 2012 GOP presidential nomination will attempt to send signals as to which commitments each candidate will sacrifice. Since so much of this signaling is non-verbal, it will be hard to pin down who truly is committed to which. But there’s a vibe. Tim Pawlenty for example seems less excited about #4 than Mitt Romney, never mind Mitch Daniels. Mike Huckabee’s voters will demand unwavering adherence to #3, which puts pressure on 1, 2 and 4.

I think this is largely true, except that #3 -- no Medicare cuts -- is more the party's attempt to compromise with the electorate than anything else. Avoiding Medicare cuts is vastly more popular with the general public than any of the other three goals. That's the primary weapon the party used against health care reform.

If Republicans could enact their dream agenda with no public accountability whatsoever, they'd slash Medicare and taxes (primarily on the rich) and keep defense spending high. But the need to avoid antagonizing voters by cutting Medicare is what makes the combination so unworkable.