Another problem that could prove embarrassing for Democrats: Under Senate rules, any Senator can bring a budget resolution to the Senate floor if the majority has failed to do so after May 15.
Therefore, Republicans could force Democrats to vote to proceed to their own budget whether the majority wants to or not. Senate Minority Leader Mitch McConnell (R-Ky.) already used the maneuver when he forced a vote on Obama's budget earlier this year.
Democrats would be in a position of either rejecting their own budget or — perhaps even worse for them — voting to take it up and having their sizable contingent of vulnerable incumbents face an onslaught of politically charged amendments.
Several aides said they wouldn't be surprised if Conrad ultimately holds off on presenting his plan after briefing leaders and the rest of the Democratic Conference on it today.
In the meantime, Senate Majority Leader Harry Reid (D-Nev.) gave up Tuesday on his plan to proceed with a resolution authorizing U.S. military involvement in Libya after Republicans objected. GOP Senators argued that the reason for canceling this week's recess was to deal with the budget and the debt limit.
Republicans, led by Sen. Ron Johnson (Wis.), said they would object to any legislation not dealing with the debt and the budget until the matter is settled.
"The Senate is basically fiddling while America goes bankrupt," Johnson said during a hastily called Tuesday afternoon press conference.
In lieu of the Libya resolution, Reid on Tuesday filed a motion to limit debate on his nonbinding resolution calling for people making more than $1 million a year to contribute to deficit reduction.
The measure is intended to highlight Democrats' call for the elimination of tax breaks for the wealthy, but the Sense of the Senate resolution does not propose any specific tax changes. Still, Democrats are considering holding votes on the variety of tax breaks they spotlighted last week.
The GOP will have its opportunities to put Democrats on the spot, too.
"They better be careful what they wish for on this," a senior GOP aide said.
And McConnell noted that taxes on luxury items such as yachts backfired in the early 1990s, when thousands lost their jobs before the tax was rescinded.
Obama, for his part, invited leaders from both chambers to the White House on Thursday and said he wants a deal on the debt in the next two weeks.
He rejected talk of a short-term deal that Republicans have been floating as of late.
"I don't think the American people sent us here to avoid tough problems. ... We've got a unique opportunity to do something big," he said.
He continued to insist on a "balanced" approach that includes eliminating tax breaks for the wealthy and corporations.
Senate Minority Leader Mitch McConnell, R-Ky., carries a musket on stage as he speaks during the American Conservative Union's Conservative Political Action Conference (CPAC) at National Harbor, Md., on Thursday March 6, 2014.