A Tuesday markup is not possible due to a 48-hour advance notice rule in the committee.
The fact that Democrats will meet with Obama on Wednesday and Republicans will meet with him Thursday rules out those dates since committee members will be at the White House.
A two-day markup is additionally unlikely to begin on a Friday.
Conrad's office did not respond to a request for comment. The chairman is under pressure to move a resolution that under law should have been agreed to by both House and Senate by April 15.