I would argue that Reagan's major achievement in office for which the US had to pay a price was Reagan's policy of cutting taxes.
When Ronald Reagan came to office, he wanted to cut taxes. He felt that taxes constituted a drag on the US economy and he believed that a cut in taxes would spur economic growth. Reagan was able to get a substantial tax cut passed during his first year in office. However, Reagan did not manage to combine the tax cut with any budget cuts. This meant that the government ran a large deficit during Reagan's time in office. One can argue, then, that Reagan's tax cuts were an achievement, but one that was paid for by an increased level of government debt. This is a problem that still haunts us today.