UPDATED: The WGA and AMPTP have ended talks for today and are expected to resume bargaining at 10 a.m. PT on Monday. Sources close to the situation report there was some progress on the issue of short-order series compensation and in closing the gap on the funding needed for the WGA’s over-taxed health insurance plan.

PREVIOUSLY: Top leaders of Hollywood’s major TV players held a conference call Sunday morning to discuss the state of the WGA contract negotiations as worries mount about the potential for a strike to begin on Tuesday.

The Alliance of Motion Picture and Television Producers made several new offers to the WGA during Sunday’s afternoon negotiating session. The studios are now waiting to hear when the guild expects to respond to the latest proposals.

The sides are facing a midnight PT Monday deadline to make a deal before the current contract expires. The WGA has said it will strike on Tuesday if there is no deal in place, although there is precedent for a short-term extension if the sides feel they are making progress. The Sunday bargaining session is a sign of the urgency for both sides.

Earlier in the day, CBS chief Leslie Moonves, Warner Bros.’ Kevin Tsujihara, Fox Networks Group’s Peter Rice, NBCUniversal’s Steve Burke, Disney/ABC TV Group’s Ben Sherwood, Sony’s Michael Lynton, and Paramount’s Jim Gianopulos held a conference call to discuss the situation and the state of the bargaining. Sources close to the situation say the CEOs of AMPTP member companies are frustrated by what they view as a lack of engagement by WGA leadership in the typical give and take of dealmaking.

Meanwhile, sources indicate that the sides have made progress on the crucial issue of funding for the WGA’s health plan. That movement in closing the gap between the AMPTP’s offer and the WGA’s ask in recent days was seen as a hopeful sign by the CEOs that there is common ground to be found on the other sticking points.

The CEOs are keeping a close eye on the talks in an effort to avoid the leadership failures of 2007, when the lack of senior management engagement early on in tough negotiations set the industry on course for a crippling 100-day strike.

In 2007, the wrangling over the WGA’s digital jurisdiction, residual, and royalty structures for new media distribution was complicated because those markets were just beginning to take shape. But the AMPTP’s effort to delay discussions about compensation for digital distribution of TV programming — at a time when networks were already making full episodes available online with advertising and paid downloads — was a tactical blunder that enraged WGA members, setting the stage for the work stoppage.

This time around, from the CEOs’ perspective, the issues are complicated but not insurmountable. Sources emphasized that the key decision-makers at AMPTP member companies have been briefed regularly on the nitty-gritty of the talks. There is unanimous support at the top for addressing the WGA’s demand that the studios adjust compensation formulas for writers working on short-order series. There is an understanding that the shift in TV series production away from the traditional broadcast model of 22 episodes per season to shows that run 6-13 episodes per season has taken a big bite out of writers’ paychecks.

“These are solvable issues,” said one senior executive closely involved in the talks.

The source emphasized that unlike the dynamic in 2007, there is no hawks vs. doves divide among the companies on the key issues. The leaders of the AMPTP memberes want to make a deal, albeit one that they can live with from a financial standpoint. As always in Hollywood labor negotiations, the studios have to calculate the costs of contract gains not just with the WGA, but multiplied by three other unions — DGA, SAG-AFTRA, and IATSE — who will be sure to seek similar terms under the industry’s tradition of pattern bargaining.

According to studio sources, the WGA’s initial pattern of demands put on the table when talks began in March were significantly higher than the parameters of the deal set by the DGA in December. The DGA’s traditional role in setting the template for Hollywood’s three-year labor deals has long been a source of resentment for the WGA as well as SAG-AFTRA.

The biggest hurdle at present, from the CEOs’ perspective, is that WGA leaders in the bargaining room have offered little feedback on the range of options for what would constitute an acceptable compromise between what the studios are offering and the guild’s initial asks. In addition to the short-order series issue, the WGA is pushing for parity on script fees, raising work done for cable and SVOD outlets to the top-tier broadcast level, and for increases in residuals to approach the broadcast benchmark.

The AMPTP has yet to take the step of making its last, best, and final offer. That is expected to come on Monday, when the deadline will be merely hours away. The hope is that the intense time pressure will break what the CEOs see as a logjam at present. There was some concern that the WGA push AMPTP negotiators to the eleventh hour and then seek negotiations directly with a few representative CEOs.

Naturally, the management side would prefer the issues be hammered out by the labor pros in the room. But if push comes to shove, there is clear motivation at the top to avoid a work stoppage that would undoubtedly be painful for all constituencies.

“All of us are dealmakers — that’s what we do,” said one source close to the situation. “We know a lot of the (WGA) people across the table. We just need someone to tell us what they really need to get this done.”