WASHINGTON — Senate Republicans took a significant step toward passing a sweeping tax overhaul on Tuesday, with a key panel giving its approval and several wavering senators indicating they would support the tax package, helping clear the way for full Senate consideration later this week.

Passage of the tax overhaul, which seemed uncertain on Monday, strengthened considerably on Tuesday after the Senate Budget Committee voted along party lines to advance the plan. A flurry of last-minute deal making helped garner the support of a few Republican lawmakers who had expressed concerns about the $1.5 trillion package, including its treatment of small businesses and its effect on the deficit.

The rapid turnaround underlines the pressure Republicans face to pass a tax cut and notch a significant legislative victory in their first year controlling both Congress and the White House. To help push the effort forward, President Trump went to Capitol Hill on Tuesday for a lunch meeting with Republican senators, where he made promises to some and admonished another.

“I think we’re going to get it passed,” he said later at the White House. “It’s going to have lots of adjustments before it ends, but the end result will be a very, very massive — the largest in the history of our country — tax cut.”