Under Carter, federal revenue was steadily increasing in spite of our economic troubles at the time. After the Reagan tax cuts went into effect, there was a large dip in revenue that we never recovered from even though revenue began to rise again. By the end of the Reagan years, the deficit and federal debt had ballooned out of control. By the end of G. H. W. Bush's presidency, the destructive policies of Reagan and Bush had finally culminated in a recession. Clinton saved us, and by the end of his second term, we actually had a budget surplus! Afterwards, G. W. Bush and the Republicans in congress ran deficit back up again and along with Wall Street, created another recession that Obama is now doing his best to fix. Conclusion: Democrats are better for the economy and the deficit than Republicans.
I can't remember all the places I have heard bits of this story over the course of my lifetime, but I know that more can be found here.
The Republicans' story:
Under Carter, the economy was in shambles. Following the example of J. F. K., Reagan cut taxes and the economy grew. As predicted by economist Art Laffer, the economy grew so much that revenue actually increased even under the lower tax rate. Now everyone could have their pie and eat it too! Unfortunately, the Democrats in congress (which control spending) started spending much more, driving up the deficit. Later, G. H. W. Bush broke his "no new taxes" pledge and gave into the Democrats, thus hurting the economy (which may have been suffering from a natural cyclic recession anyways). Clinton and the Democrats were making things much worse until the Republicans took congress in 1994. Controlling the spending, the Republicans resisted Clinton's big government plans and six years later brought down the deficit. By this time, another recession had begun (naturally), but the Clinton administration was "cooking the books" to make it seem less than it was. G. W. Bush won anyways and cut taxes again, saving us from that recession. Then, due to the Republicans acting like Democrats and spending too much (although, to be fair, much of that spending was on the war and therefore deemed justified by many) we ended up with a deficit again. Now Obama has taken those mistakes and made them much much much worse. Conclusion: You can't always trust all Republicans, but "conservative" economic policies work.
I can't rember all the places I have heard bits of this story over the course of my lifetime, but I know that more can be found in Rush Limbaugh's 1993 book, See I Told You So.
For our recent economic problems, see my earlier post Opposing Narratives To The Current Economy.