The Senate is slated to vote Tuesday on three competing plans to battle the virus, with a bipartisan plan that cuts Obama's $1.9 billion request to $1.1 billion having the greatest chance to advance.
The Centers for Disease Control and Prevention recommends that pregnant women not travel to areas with Zika and that if they live in a Zika area to strictly follow steps to prevent mosquito bites and to prevent sexual transmission.
The White House and its Democratic allies have been sharply critical of Republicans controlling Congress over delays in providing additional funds, which they say is required for mosquito control, purchasing diagnostic tests and developing and manufacturing a vaccine.
House Republicans on Monday unveiled their Zika proposal, which would slice Obama's request to $622 million and pair it with offsetting spending cuts to unspent Ebola funding and leftover money at the Department of Health and Human Services.
McConnell set up a series of votes, first on an alternative Senate plan by Florida Democrat Bill Nelson and his home-state GOP colleague Marco Rubio that largely mirrors Obama's request.