The gears are beginning to turn in a way that could launch formal bicameral talks to raise discretionary spending caps for the next two fiscal years.

At the start of the fiscal 2020 budget resolution markup Wednesday, Senate Budget Chairman Michael B. Enzi said the House Democratic leadership reached out to him a day earlier to discuss legislation to increase the caps.

A Democratic aide said Enzi and House Majority Leader Steny H. Hoyer, of Maryland, saw each other in passing at an event and discussed getting a caps deal, but the aide said the conversation was not “substantive.”

House Democrats are wrestling with their own internal spending caps discussions, and still need to round up votes to pass a bill in that chamber that can bring together the moderate and liberal wings of the party. If party leaders are seen as already negotiating with Senate Republicans, it could cause problems with the rank-and-file among House Democrats.

Enzi said he suggested also dealing with the statutory debt limit, which needs to be lifted by late September or early October, and budget process changes in any package that would raise the spending caps for fiscal 2020 and 2021. Enzi said such provisions “could be done in one package and have some chance of passing.”

“I think that they were serious,” Wyoming Republican said about his conversation with Democrats.

House Budget Chairman John Yarmuth has been formulating proposed increases in the defense and nondefense caps that could win majority support in the committee and on the floor, most likely in the form of a regular bill to raise the caps.

“What we’re trying to do is two things,” the Kentucky Democrat said Wednesday. “One is provide some numbers so the appropriators can do their work, and then simultaneously establish our negotiating starting point as we move toward the Senate corner.”

Yarmuth said he is leaning against marking up a budget resolution because “the odds of our being able to pass a budget resolution on the floor are not as great as other options.”

During opening remarks on the Senate budget resolution, Health, Education, Labor and Pensions ranking member Patty Murray decried the lack of a proposal in the document to raise the spending caps.

The Washington Democrat said she filed an amendment to be considered during the markup Thursday that will “make clear the intent of Congress [to] work to reach another two-year deal on the caps that maintains parity in adjustments between defense and nondefense spending.”

As Senate Budget chairwoman in 2013, Murray wrote a fiscal 2014 budget resolution that recommended an increase in the caps while technically proposing spending limits in line with the statutory caps as required under budget law.

She said her proposed increase “set up the eventual negotiations” with then House Budget Chairman and Wisconsin Republican Paul D. Ryan that led to the first two-year agreement to raise spending caps set under a 2011 deficit reduction law.

The 1974 law establishing the modern budget process allows a point of order to be raised against a budget resolution that exceeds statutory spending caps.

Enzi said he did not propose alternative cap increases because “the Budget Act doesn’t call for us to do that, and I tried to stay within what the Budget Act says, because that’s the law.”

Enzi added, “It doesn’t take wording in here to suggest that we need to do something with the caps and with the debt limit and with the budget process.”

Murray said she also filed amendments to strike reconciliation instructions in the budget resolution calling for $94 billion in deficit savings over five years.

Those instructions are unlikely to be used since the House and Senate are unlikely to agree on a budget resolution. Nevertheless, Murray said the reconciliation instructions could harm her negotiations with Senate HELP Chairman Lamar Alexander, R-Tenn., to reauthorize higher education law.

The page for the draft fiscal 2020 Senate budget resolution is here.

The page for the not-yet-introduced draft fiscal 2020 House budget resolution is here.

Lindsey McPherson contributed to this report.