Why not save the list  as a template with content and then create a list from the
template in your new site?

You can try using Sharepoint Designer's Import and Export Package
option(fwp).

Can you save it as a template with the data then install it on the other
site?

When I try to export  the list  (TASKS) I receive an error related to a
size limit has been exceeded. I am using Microsoft SharePoint Designer
and when I export it I get an error related to size limit exceeded.

Here is the exact error message no matter what remote site  I am
connected to using Microsoft SharePoint Designer 2007

The site is too large to save as a template. The size of a template
cannot exceed 10485760 bytes.

Whether you are using the user Interface Save List as Template or SPD there
is a default size limit on template files of 10 MB. (10,485,760 Bytes).
There is an stsadm  command that let you increase the maximum template size
allow to approximately 500MB. You can find an explanation on this Blog.

jshenry.typepad.com/.../increase-stsadm.html

I just posted that after finding it. Does this need to be
ran on the source site  because that is the limitation of the company
currently hosting  the site from which we are moving from and they don't
want to use the STSADM utility. Also, the funny thing is that the list
doesn't exceed this limitation but perhaps the whole site does I am
sure. I believe the total size of the TASKS is much less than 10MB.
That is why I am confused. I am trying this using another site as a
test and know the TASKS doesn't exceed this size. Does this apply to
the entire site size of the source?

I appreciate and value your time man. This whole group is fantastic for
bouncing issues like this off from due to the level of expertise each
one of us shares.

The 10 MB limit is for the list  and its attachments, not the overall
site.

The command gets run on the server, and increases the max size available for
any template on the server, not on a site  by site or list  by list basis.
You said you are doing this in SPD. In that case are you sure you are
saving just the list and not the whole site as a template? You can do the
same thing from inside the list settings in the UI and then you'll be sure
you are getting just the list. Just go to the List Settings for the Task
list you want to save and use the Save List as template link. Then go to
the new site and create a new Task list based on the template you created.

You only want to save the list, not the site. Do this from the Task list, list
settings page. If you are sure the list  has less than 10mb of content you should
be ok.

I don't know if I found the right solution nor do I know what site  to
run this on if it is the source or the destination. I would assume I
need to run this on the source?

stsadm -o setproperty -propertyname max-template-document-size
-propertyvalue 50000000