Senate appropriators are moving forward with spending bills for the next fiscal year, even without a House-Senate agreement on the budget.

Appropriations Chairwoman Barbara A. Mikulski told CQ Roll Call she’s setting a goal of finishing the committee process before the August recess. She plans to meet with subcommittee chairmen (known in appropriations parlance as “cardinals”) next week to go over the amounts they have to spend on their respective bills, known as 302(b) allocations.

“I look forward to sharing ideas and allocations with my subcommittee chairmen next week and encourage them to begin to mark up their bills at $1.058 trillion,” Mikulski said. “We’ll have a meeting in June of the full committee in which we’ll have a vote on our allocations.”

The Maryland Democrat is making a renewed push to return the Senate to a more orderly process of considering spending bills that isn’t as dependent as catch-all omnibus bills and stopgap continuing resolutions. In conversations with reporters, Republican appropriators have expressed optimism that Mikulski’s efforts could bear fruit.

Mikulski’s predecessor, the late Daniel K. Inouye of Hawaii, would often speak of how running the government on stopgap laws is less than ideal, but he could not overcome the political inertia against “regular order.”

Speaking at a subcommittee markup earlier Wednesday, House Appropriations ranking member Nita M. Lowey wasn’t too optimistic about restoring normalcy.

“This imperils this year’s appropriations process, making it nearly impossible to move all 12 bills. Instead, we will likely see a few bills given reasonable allocations while others are left in limbo indefinitely until we pass a CR,” the New York Democrat said.

In recent days, Senate Republicans have resisted a number of Democratic efforts to get the competing budget resolutions from the House and Senate into a conference committee. The latest such floor exchange came Wednesday, when Sen. Ron Wyden, D-Ore., sought unanimous consent to do so and Minority Leader Mitch McConnell, R-Ky., objected after Wyden declined a request to require the conference to reject any deal that would increase the debt limit or taxes.

Majority Leader Harry Reid, D-Nev., had told reporters last week that he planned to meet with Mikulski and Budget Chairwoman Patty Murray of Washington to discuss the appropriations matter. Murray is also a member of Democratic leadership and chairwoman of the Transportation-HUD Appropriations subcommittee.

This time, the Senate’s first fight may be over the top-line number at which the bills are written. Some GOP senators may balk at the $1.058 trillion spending level. Republican aides say they prefer to consider bills at a lower spending level that builds in continued implementation of the spending cuts required by sequestration.

“We hope to have the regular order and have all of our bills marked up and through the full committee by Aug. 1,” she said, adding that she hopes to get some of the bills through the floor as well.