Supporters of a bill that would broaden states’ ability to collect sales tax on online purchases acknowledge they face a tough battle in the House.

The measure, called the Marketplace Fairness Act, appears on a glide path toward passage in the Senate, with a final vote likely in early May.

But while Democratic leaders in the Senate supported the bill enough to bypass the Finance Committee and bring it straight to the floor, the GOP brass in the House has so far shown little interest in the measure.

The issue has received such scant attention in the lower chamber that neither Speaker John Boehner (R-Ohio) nor Majority Leader Eric Cantor (R-Va.) has taken public positions on it.

A Boehner spokesman deferred to House Judiciary Chairman Bob Goodlatte (R-Va.), whose panel has jurisdiction over the online sales tax bill, and a spokesman for Cantor, Doug Heye, said only: “We’ll review what the Senate sends over.”

The House is also unlikely to follow the Senate’s lead in sidestepping the committee process on the online sales tax bill – and Goodlatte, with Boehner’s blessing, has taken the lead in raising concerns about the legislation.

“We do have a ways to go,” Rep. Peter Welch (D-Vt.), a sponsor of the bill, told The Hill on Friday. “But we’re also much further along than we were a couple of years ago, or even a couple of months ago.”