I believe if the politicians listen to the voice of the people across the United States, as they should, then Congress should have plenty of votes to approve a federal marriage amendment. This shouldn't have to pass to the states for consideration, it could be changed on a federal level.
Congress doesn't have enough votes right now to authorize a federal marriage amendment for approval to the states. Senate Democrats will block the move even if House Republicans approve the measure. Until both chambers are in control of one party, there won't be much done in the way of constitutional amendments unless a huge consensus is reached in Congress.
While the majority of the US populations favors marriage equality the membership of the Congress is locked on the politically popular views of the religious right. Until the membership of Congress changes to reflect the views of the majority a constitutional marriage amendment is not in the works. I would expect it to be at least ten years before such an amendment is considted by the US Congress.
Marriage equality is gaining steam, but still has a way to go before it is accepted in the older, more conservative demographics that make up most of Congress. For now, it remains a state by state issue except for when the Supreme Court gets involved. It will be a few years before Congress gets more involved.
Right now anything that either the democrats or republicans try to get pushed through is going to be shut down by the other side, and neither side will work to help the other get a bill pushed through. So no I do not think they could get the votes to push it through.