If changesets on default have ancestor changesets on other branchs you have to push those changesets too. It’s not possible for a changeset to exist in a repo without all of its changesets also existing.
So try:
hg push --branch default --new-branch
which says “yeah, I know this push sends across a branch name that the remote repo hasn’t previously seen before” (it also requires Mercurial 1.6 or later IIRC)>
Also, you can take those inactive heads and make them closed heads with:
hg update thebranch
hg commit --close-branch -m 'closing'
Because “named branches are forever” many folks choose to reserve them for long lived concepts like “stable” and “experimental” and use bookmarks, anonymous branches, or clones for features, releases, and other transitory things. See this for a guide on those other options.