No, it means that President Bush is allied with the Republican Senate over the the Republican House on this ONE issue. The Democrats want to IMPEACH President Bush. To say without any qualification he is allied with them is false, period.
No, he's not even allied with the Republican Senate - only about a third of the GOP voted against the border security first resolution.
For Bush to get his way, he needs the nearly full support of the Dems in both houses. That alone shows he is wrong on this issue.