As a practical matter, Ryan, a former chairman of the House Budget Committee, doesn't need a budget. The two-year fiscal deal that his predecessor, John Boehner, negotiated before stepping down set overall federal spending level for the next fiscal year.
But the budget drama is a big political black eye for Ryan and his top lieutenants who promised a return to "regular order" under his leadership.
Completing a budget would have allowed them to lay down markers on big policy changes and give a potential Republican president the chance the move quickly in 2017 on plans to simplify the tax code, replace Obamacare and make significant changes to Medicare and Social Security.
Instead, Ryan has been wrestling for months with conservatives in the House Freedom Caucus, most of whom opposed the budget deal brokered by Boehner. Without support from some in this group, no GOP budget can pass -- and the clock is ticking.
Under budget rules, the House and Senate have until Friday to approve a fiscal blueprint, but no vote is scheduled. House members return Tuesday, and aides and members report little progress was made over the long spring break recess to break the impasse.
"Both sides are too far part at this point to suggest we'll make an April 15 deadline," North Carolina GOP Rep. Mark Meadows, a member of the Freedom Caucus, told CNN in a phone interview.
The tumult comes as Ryan is at the center of speculation that he might emerge from the Republican National Convention this summer as a consensus presidential nominee if the party can't unite behind Donald Trump or Ted Cruz. Ryan formally ruled out that prospect
Meadows said there are still ongoing talks to see whether there's an alternative plan that achieves significant savings from changes to Medicare or food stamp programs that would move separately from the budget.
But even if GOP leaders move a so-called "sidecar" bill, many conservatives say that's not good enough because there's no guarantee the Senate would even take it up and the budget they don't like would still move forward without the cuts they want.
South Carolina GOP Rep. Mick Mulvaney, a fiscal conservative who has been pushing for deeper spending cuts, told CNN "part of the reason that many Republicans are balking (on the budget) is not just because of the number but because we see it being meaningless."
He said during his tenure in Congress, not one appropriation bill has been enacted into law. Instead, he complained that members vote year after year on stopgap spending bills or a "cromnibus" that rolls several bills and policy changes into massive legislation. He's holding out some hope that the GOP-led Senate can pass appropriations bills that he and other House Republicans can consider so Congress can return to the regular process on annual spending bills.
Leadership aides and conservatives tell CNN there are still efforts this week to discuss action on the budget.
"No final decisions have been made. The chairman looks forward to continuing to work with his colleagues to advance a balanced budget that promotes common-sense, conservative solutions to the nation's fiscal, economic and national security challenges," William Allison, a spokesman for House Budget Committee Chairman Tom Price, told CNN.
But conservatives continue to stress that they never liked the deal Boehner cut, didn't vote for it, and without a guarantee that they get major cuts to mandatory programs attached to a must-pass bill, they are reluctant to back a budget on the House floor.
"Boehner called it cleaning the barn, Paul Ryan called it a crap sandwich, now we're supposed to vote for it? That's quite an ask," GOP Rep. Dave Brat of Virginia told CNN. He blamed Senate Republicans for stalling action on a budget to help protect some of those facing tough re-election races from having to take some tough votes.
Implications for Ryan
Although many of the Republicans CNN interviewed concede it doesn't send a good message that their party can't rally around a budget proposal, they don't hold Ryan personally responsible or believe there will be any serious fallout for him. Many cite his efforts over several months to listen to input from members, and privately and publicly saying he won't shove any plan down their throats.
The speaker made it clear in private sessions that it's his preference to pass a budget and start action on the dozen spending bills so Republicans could put their stamp on federal agencies' funding priorities, and work to add restrictions to programs they oppose. But he's also repeatedly stressed that he's not a dictator and said if members couldn't come to an agreement, it wouldn't be the end of the world if they skipped a budget this year.
"Some would view it as a positive," Meadows told CNN, praising Ryan for the hours he has spent listening to members' concerns and trying to find common ground, adding, "In times in the past, there would have been a forced vote. And because there is not a consensus from the bottom up, he has not done that."
Brat told CNN that not passing a budget sends the wrong signal. "Conservatives are upset at us, and the American people are upset at us," he said, and said the only way Republicans can impact the Obama administration's policies is through the power of the purse.
Normally, the internal food fights inside the House GOP have generated more outrage from fuming conservative activists who want GOP leaders to take a harder line. But the contentious 2016 battle for the Republican presidential nomination is sucking up most of the oxygen for those activists this spring.
"Not a single person has asked me about the budget," Mulvaney told CNN, stressing he held more than 30 events with constituents over the spring recess in his district.