B737-700
Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 120
Situational Awareness; Communication Breakdown
ATC Issue All Types; Conflict Ground Conflict; Critical; Ground Incursion Runway
Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action; Flight Crew Executed Go Around / Missed Approach
Airport; Human Factors; Procedure
Our taxi clearance was; 'Taxi to Runway 30L; via Y; C; M; and hold short of 4 on C.' While on Y; Ground Control told us to 'keep your speed up to cross Runway 4 on Charlie. Company [aircraft] on a four-mile final.'  I could not maintain or increase my speed because I still had two turns to make in order to cross Runway 4 (from Y onto C and a slight jog crossing 4). The company on final looked close. I asked the First Officer to confirm with Ground Control that we were definitely cleared to cross but he received no response. I was already slowing and; when no response was received; I opted to stop but could not do so in time and went past the hold short line 10 or 15 feet. We then saw a small prop on takeoff roll. The First Officer told Ground we were past the hold short line but; again; got no response from Ground. I got on the radio and forcefully reiterated that we were past the hold short line. (Company was now on short final.) Ground said; 'Just hold where you are.'  The other carrier continued its takeoff roll past us and the company was now on the go [around]. Ground then cleared us to cross Runway 4 and taxi C; M; to Runway 30L. Nothing else was said to us and our takeoff was uneventful. If you have what you believe to be a clearance; but it doesn't look right; stop; preferably; in time not to cross the hold short line. ATC needs a better choice of words. 'Keep your speed up to cross' is not a 'cleared to cross' but certainly can be construed as such given the circumstances.
[No substantive additional information was included in the secondary narrative.]
An attempt by Ground Control to expedite operations resulted in the reporter's aircraft crossing the hold short line and stopping while another continued its takeoff despite the encroachment and a third on short final executed a go-around.