Democrats and Republicans will need to bridge a $91 billion gap on budget plans before they can clear any new spending laws. But for now, neither side is suggesting a compromise — even as both contend they want a more orderly appropriations process.

“Spending is the problem, so moving higher doesn’t make much sense to me,” Sen. Mike Johanns of Nebraska, a GOP appropriator, said Tuesday. He added it would be a “tough sell” to support a higher spending cap.

Democrats, including President Barack Obama and Senate Appropriations Chairwoman Barbara A. Mikulski of Maryland, are pushing to replace the sequester dictated by current law and reset the cap on fiscal 2014 regular discretionary spending to $1.058 trillion. If the sequester’s automatic spending cuts are not replaced, fiscal 2014 discretionary spending would drop to $967 billion from about $984 billion for fiscal 2013.

Sen. Jeff Sessions of Alabama, the ranking Republican on the Senate Budget Committee, said he would fight efforts to change the spending caps.

“To come off that number is unacceptable,” Sessions said. “I would oppose it, and I think it has no chance of becoming law.”

Still, Democrats will seek to end the sequester as part of the bargaining around a larger budget deal that they hope will emerge in the next set of negotiations on the debt limit. The spending limit also is a point of contention between the House and Senate versions of the fiscal 2014 budget resolution.

And the partisan split over spending is becoming apparent as appropriators prepare to write the 12 annual spending bills. Senate appropriators want to allocate dollars based on the higher spending, while House appropriators plan to stick with the lower number. The different approaches are a formula for legislative gridlock.

“We don’t know what we can do yet,” said Sen. Richard C. Shelby of Alabama, the ranking member on the Appropriations Committee.

Shelby said he has been talking with Mikulski about how to begin writing the spending bills.

Mikulski has several options for trying to move the bills in the absence of a broader budget accord, including offering a somewhat lower spending cap as a compromise. She also could stick with the higher number, but that would likely cost her the support of Republicans.

Since becoming Senate Appropriations chairwoman in December, Mikulski has sought to maintain the bipartisan approach of her predecessor, the late Daniel K. Inouye, D-Hawaii, who had sought to write bipartisan bills that could win backing on the Senate floor.

Shelby on Monday said he and Mikulski need to be “realistic” and set spending levels that can pass the committee and the Senate floor, where 60 votes would likely be needed to advance them.

“We’re hoping that we can do that,” Shelby said. “It’s early, but we are determined, if we can, to make the process regular.”

If Mikulski follows Inouye’s lead, it might be late summer or fall before appropriations bills move through committee.

In 2011, Inouye waited until leaders in both parties and chambers agreed on how much to spend for fiscal 2012 in the August 2011 debt limit law (PL 112-25).

Then, by the end of the September, Inouye moved 11 of the dozen fiscal 2012 bills through his committee, attracting strong bipartisan support. Fiscal 2012 appropriations were then wrapped up in two broader omnibus packages — one cleared in November and the other in December.

It’s possible fiscal 2014 spending might eventually be wrapped up much as fiscal 2012 was if Mikulski and Shelby wait for leaders in both parties and Obama to make a final decision on spending.

Meanwhile, bills in the House are far easier to move, as the majority party has the procedural tools to pass them without any minority support. As a result, Republicans likely will move many of the bills this summer at the lower spending level.