SEPTA told Action News that since they made the most recent offer, it is up to the union to come back to the table.
Only brief meetings were held between the two sides on Sunday.
Despite fears of a strike, union President Willie Brown said workers would stay on the job and continue to negotiate. There has been no strike authorization vote so far.
"A strike is not going to happen right now so people can go to work and feel comfortable going to work for a while. I will let you know when it comes time for us to go on strike," said Brown on Sunday.
All SEPTA buses, trolleys and trains were running on schedule Monday morning.
The failure to reach a deal Sunday came after several days of public optimism from both sides. Brown said Thursday night "we are close," and SEPTA officials indicated going into the weekend that progress was being made.
But by Sunday afternoon, things appeared to have shifted.
Negotiators sat inside the Sheraton Hotel for hours Sunday with the groups only coming face-to-face for actual talks for several minutes at a time.
Sources tell Action News the union wants a two-year deal with wage increases, no increase in workers' contributions to healthcare benefits and no changes to the pension system.
SEPTA is offering a pay increase of 2 percent the first year and 3 percent the second year, with a 1 percent increase in healthcare contributions.
"We're ready to sign a deal limited to those terms but the union has refused. We urge the union to get back to the table," said SEPTA spokeswoman Jerri Williams Sunday night.
"This comes down to classism," said Brown. "If what I'm asking for is so outrageous, how do they have it? I'm asking for no more than what they have. In fact, if they give us everything that we're asking for, we still won't have what they have."
In its 49-year history, SEPTA has had at least 12 strikes. Some have been long and bitter.
In 1995, frustrated SEPTA workers tied up traffic on the Schuylkill Expressway with a slow-moving, rolling roadblock.
That strike lasted 14 days. The record is a 108-day rail strike in 1983.
If SEPTA's unions strike, the following will STOP running:
- Broad Street Line
- Market Frankford Line
- Norristown High Speed Line
The Regional Rail lines and the LUCY bus will continue to operate.