The voters get to select the President, not Congress. Right or wrong, they elected Barack Obama in 2008. Perhaps, if there had been clear proof and public consensus of Barack Obama’s foreign birth early enough in 2007, he could have been disqualified without controversy.
But as it was, there was no consensus - and a deeply partisan division on the matter.
As we are seeing right now, the Constitution’s establishment of three coequal branches makes it very difficult for the Legislative branch to override the people’s choice for President.
To suggest the Legislative branch should have “enforced” Obama out of office, against the will of the people, is just absurd.
Their only mechanism for doing so would have been impeachment and removal, and no matter how justified it may be, impeachment against the will of the people is a zero sum game - just ask the Democrats.
He was never legally "in office". They did not have to do anything but arrest him. The impeachment process only applies to the removal of a legal President, not a usurper. The Constitution itself along with the timeline of events in relationship to what the Constitution demands tells us all that he was never President no matter what Congress did or did not do.