Here is an XSLT 1.0 version, using substring-before and substring-after.
Thanks to adhocgeek for the XML input.
<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
<xsl:output method="xml" indent="yes"/>
<xsl:template match="/item">
<xsl:copy>
<xsl:apply-templates select="date"/>
</xsl:copy>
</xsl:template>
<xsl:template match="date">
<xsl:copy>
<xsl:variable name="date" select="substring-before(@value, ' ')"/>
<xsl:variable name="M" select="substring-before($date, '/')"/>
<xsl:variable name="D-Y" select="substring-after($date, '/')"/>
<xsl:variable name="D" select="substring-before($D-Y, '/')"/>
<xsl:variable name="Y" select="substring-after($D-Y, '/')"/>
<xsl:variable name="time-ampm" select="substring-after(@value, ' ')"/>
<xsl:variable name="time" select="substring-before($time-ampm, ' ')"/>
<xsl:variable name="ampm" select="substring-after($time-ampm, ' ')"/>
<xsl:variable name="h" select="substring-before($time, ':')"/>
<xsl:variable name="m-s" select="substring-after($time, ':')"/>
<xsl:variable name="m" select="substring-before($m-s, ':')"/>
<xsl:variable name="s" select="substring-after($m-s, ':')"/>
<xsl:variable name="hh">
<xsl:choose>
<xsl:when test="$ampm = 'PM'">
<xsl:value-of select="format-number($h + 12, '00')"/>
</xsl:when>
<xsl:otherwise>
<xsl:value-of select="format-number($h, '00')"/>
</xsl:otherwise>
</xsl:choose>
</xsl:variable>
<xsl:value-of select="concat($Y, '-', $M, '-', $D, 'T', $hh, ':', $m, ':', $s)"/>
</xsl:copy>
</xsl:template>
</xsl:stylesheet>
XML
<?xml version="1.0" encoding="utf-8" standalone="no"?>
<item>
<date value="4/1/2013 5:13:41 PM"/>
</item>
output
<?xml version="1.0" encoding="utf-8"?>
<item>
<date>2013-4-1T05:13:41</date>
</item>