Ms. Warren has been sharply criticized for her decision to release a DNA test in October proving that she has Native American heritage. And Mr. Sanders’s hold on the party’s progressive base may be slipping as a new generation of Democrats like Representative Beto O’Rourke demonstrate early strength in polls and straw polls, such as the one conducted this week by the liberal group MoveOn.

The two would-be candidates have made their names as outspoken economic populists and are expected to run on similar platforms, with slight differences.

The prospect of two high-profile progressives pursuing White House runs has stirred concerns among some on the left that they could cut into each other’s support, potentially letting a less progressive candidate emerge with the nomination.

A handful of liberal lawmakers on Thursday downplayed that prospect, arguing that the center of gravity in the party had shifted inexorably left. But they acknowledged that if both senators run it could force the hand of Democrats who like each of them.

“When it comes to progressives, I think Bernie and Warren are in a different league,” said Representative Ro Khanna, a California Democrat, noting that if each of them enter the race “I’ll have to decide.”

In 2016, many of Mr. Sanders’s backers bitterly complained about the Democratic establishment’s attempt to effectively crown Hillary Clinton as the nominee, making it difficult for Democrats to suggest that any potential candidate step aside or that there be any attempt at clearing the field.

“They both deserve to make up their own mind,’’ said Representative James McGovern, Democrat of Massachusetts. “It would be wrong for any of us to say, ‘well you’re the better progressive.’ We can all make up our minds, that’s what primaries are for.”