I don't think the major US parties follow any ideology at all. It's not that the views shift over time, it is that they are inconsistent at any given instant.
For example, Democrats support social welfare for minorities and the disabled; Republicans support social welfare for the elderly and veterans. To be more specific: Republicans supported the Medicare prescription drug program, while Democrats supported the ACA. This is because the elderly vote Republican, while minorities vote Democrat. This is ideologically inconsistent because Republicans claim that they are against welfare, while the Democrats will say they are in favor of it. But both parties are actually supporting welfare, just aimed only at their particular constituent groups.
Another example: Republicans generally support a strict interpretation of the second amendment, but a loose interpretation of the first. Democrats take the opposite view. There is no consistent ideology here. The reality is that Republicans are more likely to own guns, and Democrats are more likely to be employed in mass-media.
Another one: Republicans claim Obama could not be president because if he was born in Kenya, but Republicans claim that Ted Cruz can be even though he was born in Canada, and Republicans also claimed that George Romney could even though he was born in Mexico. The underlying philosophy is the definition of the term "natural born citizen" for which the party members hold no consistent ideology.
It is for this reason, that I don't see political parties as aligning to an ideology at all. The align to whatever group will vote for them. Most voters have no concept of a philosophy or ideology on these matters. They merely vote for the party that is most likely to help them out.