Text rotator je na začetku prazen

Lahko daš še eno variablo interval = 0; in flag boolean, ko je prvič daš timeInterval = 0, spremeniš flag potem pa daš vrednost 3000.

var first = true;

first ? timeInterval = 0 : timeInterval = 3000;

potem pa kjer je prvič daš

if(first) {

} else {

}

in seveda na koncu spremniš

first = false;

<script type="text/javascript" >
var intervalId;
var timeInterval = 3000;
var first = false;

var myquotes = new Array(
	'123',
	'456'
	);

function rotatequote()
{
	if(!false) {
		thequote = myquotes.shift();
		myquotes.push(thequote);		
		document.getElementById('quotetext').innerHTML = "<label onmouseover='pauseRotating()' onmouseout='resumeRotating()'>"+thequote+"</label>";
		pauseRotating();
		resumeRotating();
		first = true;
	} else {
		thequote = myquotes.shift();
		myquotes.push(thequote);		
		document.getElementById('quotetext').innerHTML = "<label onmouseover='pauseRotating()' onmouseout='resumeRotating()'>"+thequote+"</label>";
	}
}



intervalId = window.setInterval(rotatequote, (!first ? 1 : timeInterval) );	


function pauseRotating()
{
	window.clearInterval(intervalId);
}

function resumeRotating()
{
	intervalId = window.setInterval(rotatequote,Number(timeInterval));
}

</script>