An easy function to pull all details of the debug backtrace:
<?php
function getDebugBacktrace($NL = "<BR>") {
 $dbgTrace = debug_backtrace();
 $dbgMsg .= $NL."Debug backtrace begin:$NL";
 foreach($dbgTrace as $dbgIndex => $dbgInfo) {
 $dbgMsg .= "\t at $dbgIndex ".$dbgInfo['file']." (line {$dbgInfo['line']}) -> {$dbgInfo['function']}(".join(",",$dbgInfo['args'])")$NL";
 }
 $dbgMsg .= "Debug backtrace end".$NL;
 return $dbgMsg;
}
?>

Then you can call it anywhere you want to get a string with the debug backtrace in readable format (i.e. your error handling function)
<?php
$backtrace = getDebugBacktrace();
echo "Fatal error! Cannot connect to database!";
echo $backtrace;
?>

If you're running on command line, you might want to replace the line split. You can do that thru the function argument:
<?php
$backtrace = getDebugBacktrace("\n");
echo "Error! Server is running out of foos! Dumping error backtrace";
echo $backtrace;
?>

Hope that helps,
Aryel