The inability of conservatives to admit this incoherence leads them to misunderstand liberals. Liberals are not the "party of big government" as a foil for conservatives' "small government." Liberals have a set of defined policy goals that they will use any method necessary to enact. Because many of those goals involve help for the disadvantaged, often the methods include greater government involvement. But "big government" is merely the means by which liberals prefer to enact policy goals. It is not the end in and of itself. Conservatives could do a better job of influencing policy if they were to acknowledge this fact.
A good example was the health care debate. Liberals had one overarching policy goal: cover the uninsured. Wonks had a secondary goal of reducing health-care costs, so as to reduce the crippling effects of Medicare costs on the federal budget. The problem with Republican counter-proposals (such as they were) was not that they were insufficiently "big government," but rather that they didn't accomplish the policy goals that liberals aimed for. The alternatives focused on interstate insurance sales and tort reform. Partisan and non-partisan analysis showed that they did very little to accomplish either of the two major goals set out above. The ACA ended up being about as "small government" as it could be while still largely accomplishing the first goal and making inroads on the second.
We would all be better off if policy debates weren't stubbornly framed as "big government socialists vs principled advocates of small government solutions." It's simply not accurate to portray either side that way. On civil liberties and gay rights, liberals are the small government party. On health care and economic regulation, conservatives are. Each side has policy goals. They work to enact them. End of story.
EDIT: Chait writes about the same phenomenon on judicial restraint/activism:
Both parties are fairly instrumental about the law. They favor judicial activism in issue areas where they're politically weak, and support it in areas where they're politically strong. The difference is that Republicans tend to alternate their demands for judicial activism with a lot more pious declarations of fealty to judicial restraint.