House Republicans have abandoned their most recent proposal to reopen the government in exchange for changes in the Affordable Care Act on Tuesday, after House Speaker John Boehner (R-Ohio) indicated that there wasn't enough support for it.

The decision by the Republicans to abandon their proposal came only an hour after the White House on Tuesday had rejected the latest proposal from the House.

The GOP plan was a "last-gasp" effort to influence the Affordable Care Act during these current negotiations, something the President and his party have rejected outright.

"The President has said repeatedly that Members of Congress don't get to demand ransom for fulling their basic responsibilities to pass a budget and pay the nation's bills," White House spokeswoman Amy Brundage said on Tuesday.

Earlier on Tuesday, Senators from both parties said a deal was near, with Senate Majority Leader Harry Reid (D-Nevada) saying he hoped a deal could be reached sometime this week.

Two plans, in the House and Senate respectively, have the government funded through January 15, 2014 and would suspend the U.S. debt limit until February 7, 2014.

The current debt limit agreement expires on Thursday.

Reach Executive Producer Colin Hale here. Follow him on Twitter.