Since (La)TeX doesn't have a “background color” for text, you would have to put your text inside a box which you can then color. Consider the following example using \colorbox.
\documentclass{beamer}
\setbeamercolor{alerted text}{fg=white,bg=red}
\newcommand{\boxalert}[1]{{%
\usebeamercolor{alerted text}\colorbox{bg}{\alert{#1}}%
}}
\begin{document}
\begin{frame}
Hello \boxalert{World}!
\end{frame}
\end{document}
Which renders

Edit: I'm no expert in beamer internals, so the following is nothing more than a hack. However, if you would like \boxalert to work with overlays, something like the following “seems” to work:
\newenvironment{boxalertenv}{\begin{altenv}%
{\usebeamertemplate{alerted text begin}\usebeamercolor[fg]{alerted text}\usebeamerfont{alerted text}\colorbox{bg}}
{\usebeamertemplate{alerted text end}}{\color{.}}{}}{\end{altenv}}
\newcommand<>{\boxalert}[1]{{%
\begin{boxalertenv}#2{#1}\end{boxalertenv}%
}}
...
Hello \boxalert<2>{World}!
\alert<+->{Text}– Seamus Feb 17 '11 at 17:55\alert, I've also provided some sort of hack to get the new command working with overlays. – Juan A. Navarro Feb 18 '11 at 10:46