Chairman Huw Jenkins had spent part of the week in South America trying to find a managerial successor to Garry Monk, with former Argentina and Chile coach Marcelo Bielsa understood to be top of his list.
And, for all caretaker manager Alan Curtis' experience in the game, the appointment remains a pressing issue as Swansea have now only won once in 13 games and find themselves in real danger at the foot of the table.
Despite dominating for long periods, Swansea failed to put away injury-depleted opponents who have failed to win in seven games since beating Chelsea at the end of October to go third in the table.
Swansea toiled to create clear-cut chances but they felt they should have had a 62nd-minute goal when James Collins appeared to block Ki Sung-yueng's goalbound shot with his arm, referee Lee Mason unmoved in the face of home protests.
Curtis, in charge of his second game, had overseen a far more cohesive performance at Manchester City and Swansea reacted to dropping into the bottom three courtesy of Saturday's results by producing a greater sense of urgency than anything seen in the final weeks of Monk's 22-month reign.
There was a determination to get on the front foot but West Ham defended well and got bodies in the way whenever Swansea sized up shooting opportunities from distance.
But the Hammers were relieved when Andre Ayew directed Neil Taylor's cross onto the roof of Adrian's goal.
West Ham did not stir as an attacking force until Mauro Zarate sent his low 25-yard drive straight at Lukasz Fabianski and Mark Noble shot tamely wide.
But perhaps the Hammers' lack of a cutting edge was understandable as attacking quartet Dimitri Payet, Diafra Sakho, Manuel Lanzini and Andy Carroll were all missing through injury.
Swansea dominated possession but they also found chances hard to come by, their best opening arriving after 25 minutes when Bafetimbi Gomis slipped in Ki but the South Korean was foiled by the legs of Adrian.
Zarate brought a flying save from Fabianski but it was Swansea who finished the first period on top and almost opened the scoring after the best move of the half.
Ki's pass gave Gomis a sight of goal and, although his shot was mishit, Cork retrieved the situation with a cute flick which saw Ayew sidefoot wide under pressure from two West Ham defenders.
Swansea appeared to be building momentum but their play was disjointed at the start of the second half until Cork's volley produced an acrobatic save from Adrian.
Moments later Gylfi Sigurdsson set up Ki for a shot which struck the flailing arm of Collins, who had thrown himself at the ball.
Swansea players surrounded Mason but to no avail as the referee awarded a corner rather than a penalty.
West Ham had their moments in the closing quarter with Fabianski tipping over Enner Valencia's drive and Collins heading over - but there was no breaking the stalemate.
TWEET OF THE MATCH
David James @jamosfoundation - "Swansea shooting in the warm up, didn't look very good"
PLAYER RATINGS
Swansea
Lukasz Fabianski: 7/10
Angel Rangel: 6
Ashley Williams: 7
Federico Fernandez: 7
Neil Taylor: 7
Leon Britton: 8
Jack Cork: 6
Ki Sung-yueng: 7
Andre Ayew: 6
Gylfi Sigurdsson: 6
Bafetimbi Gomis: 6
Substitutes
Kyle Naughton (on for Rangel 69mins): 6
Jonjo Shelvey (on for Cork 73mins): 6
Modou Barrow (on for Ayew 83mins): 6
West Ham
Adrian: 7
Angelo Ogbonna: 7
James Tomkins: 7
James Collins: 7
Aaron Creswell: 7
Alex Song: 6
Mark Noble: 7
Cheikhou Kouyate: 6
Mauro Zarate: 6
Michail Antonio: 6
Nikica Jelavic: 6
Substitutes
Enner Valencia (on for Zarate 60mins): 6
Pedro Obiang (on for Song 72mins): 6
Carl Jenkinson (on for Antonio 85mins): 6
STAR MAN
LEON BRITTON: Set the tempo for Swansea to dominate possession by picking up the pieces in midfield and acting as the link between defence and attack
Stable influence in the last few weeks as Swansea have strived for fluency.
MOMENT OF THE MATCH
Swansea were convinced they should have been awarded a second-half penalty when James Collins got in the way of Ki Sung-yueng's goalbound drive
The ball definitely struck Collins' hand to revive the age-old argument - was it intentional or was his arm in an unnatural position?
VIEW FROM THE BENCH
Caretaker-manager Alan Curtis has certainly imposed some of Swansea's old passing game and urgency in his two matches in charge, even if a plethora of chances did not fall his side's way
West Ham boss Slaven Bilic must only hope his injured forwards get back on the pitch as soon as possible as the Hammers were toothless throughout and their absences are starting to hurt.
MOAN OF THE MATCH
Lack of quality
Perhaps understandable as Swansea were struggling for confidence after a run of one win in 12 games and have surprisingly found themselves in a relegation battle, while West Ham are in danger of running out of strikers and are not the attacking threat they were at the start of the season
But still tough to take at times.
WHO'S UP NEXT?
Aston Villa v West Ham (Premier League, December 26)
Swansea v West Brom (Premier League, December 26)
Swansea enjoyed over 70 per cent of possession and had 21 shots in total but could not find a breakthrough, and caretaker manager Alan Curtis conceded his side lacked a cutting edge.
He told Sky Sports: "Yeah I think we could all see that
It's great having the possession and at least we looked like a Swansea City side again, but maybe we could pass the ball forward quicker a little bit more.
"I think we tried to over-emphasise the fact we want to keep the ball again, that we want to pass it round, and possibly we haven't done that over the past few months.
"But certainly in terms of where we want to be this is a big step forwards."
West Ham midfielder Mark Noble said the injury-hit Hammers were pleased to come away with a point.
He said: "We expected them to come out and play well, it's always the case, I don't know why; a manager leaves and all of a sudden players work that little bit harder because they want to impress the new manager and play for their places.
"So we knew it was going to be tough today and we're happy with a point."
He added: "Swansea played very well in the first 25 minutes and then we sort of got into the game and had a few chances ourselves.
"We're keeping clean sheets, we're working hard for each other
The squad are fully together and are working hard for each other."
Source : PA
Source: PA