Do competing political parties predispose the government to provide more public services?

In my opinion, they do.  (In fact, when I was in graduate
school I had a professor who had written a paper that proved that there was less in the
way of public services down in the South where the Democratic Party dominated politics
(he wrote this a long time ago) and the Republicans were
nonexistent.)

Theoretically, this makes a lot of sense. 
What parties and their members want to do most is to appeal to voters enough that they
can get reelected.  One of the best ways, it seems, to appeal to voters is to give them
things that will make them better off financially.  That is why you see so many members
of Congress campaiging on their ability to bring pork back to their districts.  (Of
course they don't call it that, but that's what it is.)  Each party has an incentive to
provide more services, then, and no incentive to cut back on those services.  Consider
the following quote:

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Such interest-group liberalism turns logrolling
(legislators trading votes) from “a necessary evil into a virtue.” So at a state level,
when southern Minnesota legislators earmark state funds for an international volleyball
center in Rochester, there is nary a peep from their Arrowhead compatriots who expect
reciprocal support in anticipation of a photo-op at a Duluth arena expansion. Both
outstate areas support a budget-draining light-rail system between Minneapolis and St.
Paul. A combined financial obligation on all Minnesotans, these projects respectively
mean more to Rochester, Duluth and the Twin Cities than they matter to the welfare of
the state at large.

So, the
idea is that the parties have to compete for votes and they tend to feel that providing
services is a good way to get people to vote for them.

For
further information, you might want to look up stuff about a theory called "interest
group liberalism" which is connected with a man called Theodore
Lowi.