Senate Democrats plan to add billions of dollars for disaster relief to a House-authored measure to fund government when the fiscal year ends at the end of September, a move that could force House Republicans to decide whether to hold-up the must-pass bill over additional dollars for disaster victims.

The House will vote Wednesday on a continuing appropriations measure designed to fund government through Nov. 18.

House leaders have geared the bill around spending levels agreed to between the parties in the rancorous August debt deal. That move was designed to avoid the possibility of a government shutdown when the fiscal year ends Sept. 30, but has risked the ire of conservatives who would like cut deeper.

The House measure includes $3.65 billion for the Federal Emergency Management Agency’s disaster relief fund, which has run almost dry as a result of a series of tornadoes, fires and storms.

House leaders have said they are willing to revisit FEMA funding as negotiations continue between the House and Senate over spending for the remainder of the 2012 fiscal year.

But they believe it is irresponsible to include all of FEMA’s funding for the year in the short-term measure designed to cover just a few weeks of government function, particularly without offsetting the dollars with cuts elsewhere. In their version of the bill, $1.5 billion of FEMA funding, which would become available to the agency immediately upon the bill’s passage, would be balanced out with a cut to a program that offers loans to auto manufacturers to encourage the production of energy efficient cars.

Senate Democrats have been emboldened to push for more now by a rare legislative win last week, when 10 Republicans joined Democrats in approving a measure to spend $6.9 billion over the next year on disaster relief efforts.

“I was disappointed to see the House shortchanged the Federal Emergency Management Agency,” Senate Majority Leader Harry M. Reid (D-Nev.) said on the floor of the Senate Tuesday, announcing he would move to amend the House resolution with additional dollars.

“It is a real, real shortchange, by failing to provide the funding to adequately help Americans whose lives have been devastated by floods, hurricanes and tornadoes,” he said.

Democrats will need the support of Senate Republicans who backed boosted FEMA funding last week to send the bill back to the House. Assuming they get it, the House will then have to decide whether to accept the funding or reject it, as the possibility of a shutdown no one wants looms.

But the Senate does not hold all the cards. The House could leave town after adopting its continuing resolution even as the Senate debates increasing FEMA funding. Since the two chambers are not scheduled to return to Washington until after the fiscal year ends Sept. 30, that maneuverer would force the same choice on the Senate that Democrats hope to force on the House: Cave on FEMA funding or risk a government shutdown.