House GOP transportation conferees huddled late Tuesday in the office of House Speaker John Boehner, R-Ohio.
A senior GOP aide working on the transportation bill said: "We have an agreement on all the big things."
However, GOP Rep. James Lankford, a conferee, sounded less optimistic, calling the state of the bill "very precarious."
Lankford, R-Okla., said there have been concessions on both sides but there are things in the bill he still doesn't like.
A senior Democratic lawmaker involved in the talks told Fox News there has been "definite movement" and "some issues (will) likely to be kicked upstairs."
One of the issues is whether the Keystone pipeline is in or out. A source told Fox News that Keystone is out of the bill and that lawmakers will do a separate vote on it. Still, the status of the pipeline remains unclear.
There is a challenge on the GOP side of the aisle to completing this quickly.
House Republicans require that bills be posted for parts of three days before bringing something to the floor.
The funding for transportation programs expires at 11:59:59 p.m. Saturday. Therefore, The House and Senate want to get this done before the end of the week.
So if the bill is to be ready for a vote on Friday, it needs to be posted Wednesday night.
"We'll be scrambling to get it done," said the GOP aide, noting there was no discussion of a interim bill to potentially bridge the gap if necessary.
The House Republican leadership team wants to present the legislation to their rank and file members at a conference meeting Wednesday morning.
"I think our conferees are happy with it," said the Republican aide.
Significant headway appears to be have been made on the Republican demand to streamline certain construction projects without subjecting them to significant environmental impact studies.